[A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ]

On semilattice structure of {M}izar types
by Grzegorz Bancerek

ABIAN, miz file
Abian's Fixed Point Theorem
by Piotr Rudnicki and Andrzej Trybulec

ABSVALUE, miz file
Some Properties of Functions Modul and Signum
by Jan Popio{\l}ek

AFF_1, miz file
Parallelity and Lines in Affine Spaces
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

AFF_2, miz file
Classical Configurations in Affine Planes
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

AFF_3, miz file
Affine Localizations of Desargues Axiom
by Eugeniusz Kusak, Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

AFF_4, miz file
Planes in Affine Spaces
by Wojciech Leo\'nczuk, Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

AFINSQ_1, miz file
Zero Based Finite Sequences
by Tetsuya Tsunetou , Grzegorz Bancerek and Yatsuka Nakamura

AFPROJ, miz file
A Projective Closure and Projective Horizon of an Affine Space
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

AFVECT0, miz file
Directed Geometrical Bundles and Their Analytical Representation
by Grzegorz Lewandowski, Krzysztof Pra\.zmowski and Bo\.zena Lewandowska

AFVECT01, miz file
One-Dimensional Congruence of Segments, Basic Facts and Midpoint Relation
by Barbara Konstanta, Urszula Kowieska, Grzegorz Lewandowski and

ALG_1, miz file
Homomorphisms of algebras. Quotient Universal Algebra
by Ma{\l}gorzata Korolkiewicz

ALGSEQ_1, miz file
Construction of Finite Sequences over Ring and Left-, Right-,
and Bi-Modules over a Ring

ALGSPEC1, miz file
Technical Preliminaries to Algebraic Specifications
by Grzegorz Bancerek

ALGSTR_1, miz file
From Loops to Abelian Multiplicative Groups with Zero
by Micha{\l} Muzalewski and Wojciech Skaba

ALGSTR_2, miz file
From Double Loops to Fields
by Wojciech Skaba and Micha{\l} Muzalewski

ALGSTR_3, miz file
Ternary Fields
by Micha{\l} Muzalewski and Wojciech Skaba

ALI2, miz file
Fix Point Theorem for Compact Spaces
by Alicia de la Cruz

ALTCAT_1, miz file
Categories without Uniqueness of { \bf cod } and { \bf dom }
by Andrzej Trybulec

ALTCAT_2, miz file
Examples of Category Structures.Subcategories
by Andrzej Trybulec

ALTCAT_3, miz file
Basic properties of objects and morphisms. In categories without
uniqueness of { \bf cod } and { \bf dom }

ALTCAT_4, miz file
On the Categories Without Uniqueness of { \bf cod } and { \bf
dom } . Some Properties of the Morphisms and the Functors

AMI_1, miz file
A Mathematical Model of CPU
by Yatsuka Nakamura and Andrzej Trybulec

AMI_2, miz file
On a Mathematical Model of Programs
by Yatsuka Nakamura and Andrzej Trybulec

AMI_3, miz file
Some Remarks on Simple Concrete Model of Computer
by Andrzej Trybulec and Yatsuka Nakamura

AMI_4, miz file
Euclide Algorithm
by Andrzej Trybulec and Yatsuka Nakamura

AMI_5, miz file
On the Decomposition of the States of SCM
by Yasushi Tanaka

AMI_6, miz file
On the Instructions of { \bf SCM }
by Artur Korni{\l}owicz

AMI_7, miz file
Input and Output of Instructions
by Artur Korni{\l}owicz

AMISTD_1, miz file
Standard Ordering of Instruction Locations
by Andrzej Trybulec , Piotr Rudnicki and Artur Korni{\l}owicz

AMISTD_2, miz file
On the Composition of Macro Instructions of Standard Computers
by Artur Korni{\l}owicz

AMISTD_3, miz file
A Tree of Execution of a Macroinstruction
by Artur Korni{\l}owicz

ANALMETR, miz file
Analytical Metric Affine Spaces and Planes
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

ANALOAF, miz file
Analytical Ordered Affine Spaces
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

ANALORT, miz file
Oriented Metric-Affine Plane - Part I
by Jaroslaw Zajkowski

ANPROJ_1, miz file
A Construction of Analytical Projective Space
by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski

ANPROJ_2, miz file
Projective Spaces
by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski

ARITHM, miz file
Field Properties of Complex Numbers - Requirements
by Library Committee

ARMSTRNG, miz file
Armstrong's Axioms
by William W. Armstrong , Yatsuka Nakamura and Piotr Rudnicki

ARYTM_0, miz file
Introduction to Arithmetics
by Andrzej Trybulec

ARYTM_1, miz file
Non negative real numbers. Part II
by Andrzej Trybulec

ARYTM_2, miz file
Non negative real numbers. Part I
by Andrzej Trybulec

ARYTM_3, miz file
Arithmetic of Non Negative Rational Numbers
by Grzegorz Bancerek

ASYMPT_0, miz file
Asymptotic notation. Part I: Theory
by Richard Krueger , Piotr Rudnicki and Paul Shelley

ASYMPT_1, miz file
Asymptotic notation. Part II: Examples and Problems
by Richard Krueger, Piotr Rudnicki and Paul Shelley

AUTALG_1, miz file
On the Group of Automorphisms of Universal Algebra & Many
Sorted Algebra

AUTGROUP, miz file
On the Group of Inner Automorphisms
by Artur Korni{\l}owicz

AXIOMS, miz file
Strong arithmetic of real numbers
by Andrzej Trybulec

On Ordering of Bags
by Gilbert Lee and Piotr Rudnicki

BHSP_1, miz file
Introduction to Banach and Hilbert spaces - Part I
by Jan Popio{\l}ek

BHSP_2, miz file
Introduction to Banach and Hilbert spaces - Part II
by Jan Popio{\l}ek

BHSP_3, miz file
Introduction to Banach and Hilbert spaces - Part III
by Jan Popio{\l}ek

BHSP_4, miz file
Series in Banach and Hilbert Spaces
by El\.zbieta Kraszewska and Jan Popio{\l}ek

BHSP_5, miz file
Bessel's Inequality
by Hiroshi Yamazaki , Yasunari Shidama and Yatsuka Nakamura

BHSP_6, miz file
On Some Properties of Real {H}ilbert Space, {I}
by Hiroshi Yamazaki , Yasumasa Suzuki , Takao Inou\'e and Yasunari Shidama

BHSP_7, miz file
On Some Properties of Real {H}ilbert Space, {II}
by Hiroshi Yamazaki , Yasumasa Suzuki , Takao Inou\'e and Yasunari Shidama

BILINEAR, miz file
Bilinear Functionals in Vector Spaces
by Jaros{\l}aw Kotowicz

BINARI_2, miz file
Binary Arithmetics. Addition and Subtraction of Integers
by Yasuho Mizuhara and Takaya Nishiyama

BINARI_3, miz file
Binary Arithmetics. Binary Sequences
by Robert Milewski

BINARI_4, miz file
A Representation of Integers by Binary Arithmetics
and Addition of Integers

BINARI_5, miz file
On the Calculus of Binary Arithmetics
by Shunichi Kobayashi

BINARI_6, miz file
On the Calculus of Binary Arithmetics, Part {II}
by Shunichi Kobayashi

BINARITH, miz file
Binary Arithmetics. Addition
by Takaya Nishiyama and Yasuho Mizuhara

BINOM, miz file
The Binomial Theorem for Algebraic Structures
by Christoph Schwarzweller

BINOP_1, miz file
Binary Operations
by Czes{\l}aw Byli\'nski

BINOP_2, miz file
Binary Operations on Numbers
by Library Committee

BINTREE1, miz file
On Defining Functions on Binary Trees
by Grzegorz Bancerek and Piotr Rudnicki

BINTREE2, miz file
Full Trees
by Robert Milewski

BIRKHOFF, miz file
Birkhoff Theorem for Many Sorted Algebras
by Artur Korni{\l}owicz

BOOLE, miz file
Boolean Properties of Sets - Requirements
by Library Committee

BOOLEALG, miz file
Boolean Properties of Lattices
by Agnieszka Julia Marasik

BOOLMARK, miz file
Basic Concepts for Petri Nets with Boolean Markings.
Boolean Markings and the Firability/Firing of Transitions

BORSUK_1, miz file
A Borsuk Theorem on Homotopy Types
by Andrzej Trybulec

BORSUK_2, miz file
Introduction to Homotopy Theory
by Adam Grabowski

BORSUK_3, miz file
Properties of the Product of Compact Topological Spaces
by Adam Grabowski

BORSUK_4, miz file
On the Decompositions of Intervals and Simple Closed Curves
by Adam Grabowski

BORSUK_5, miz file
On the Subcontinua of a Real Line
by Adam Grabowski

BORSUK_6, miz file
Algebraic Properties of Homotopies
by Adam Grabowski and Artur Korni{\l}owicz

BROUWER, miz file
Brouwer Fixed Point Theorem for Disks on the Plane
by Artur Korni{\l}owicz and Yasunari Shidama

BVFUNC10, miz file
Propositional Calculus for Boolean Valued Functions, VI
by Shunichi Kobayashi

BVFUNC11, miz file
Predicate Calculus for Boolean Valued Functions, III
by Shunichi Kobayashi and Yatsuka Nakamura

BVFUNC13, miz file
Predicate Calculus for Boolean Valued Functions, V
by Shunichi Kobayashi and Yatsuka Nakamura

BVFUNC14, miz file
Predicate Calculus for Boolean Valued Functions, { VI }
by Shunichi Kobayashi

BVFUNC24, miz file
Predicate Calculus for Boolean Valued Functions, (12)
by Shunichi Kobayashi

BVFUNC25, miz file
Propositional Calculus for Boolean Valued Functions, {VII }
by Shunichi Kobayashi

BVFUNC26, miz file
Propositional Calculus for Boolean Valued Functions, {VIII}
by Shunichi Kobayashi

BVFUNC_1, miz file
A Theory of Boolean Valued Functions and Partitions
by Shunichi Kobayashi and Kui Jia

BVFUNC_2, miz file
A Theory of Boolean Valued Functions and Quantifiers with
Respect to Partitions

BVFUNC_3, miz file
Predicate Calculus for Boolean Valued Functions, { I }
by Shunichi Kobayashi and Yatsuka Nakamura

BVFUNC_4, miz file
Predicate Calculus for Boolean Valued Functions, II
by Shunichi Kobayashi and Yatsuka Nakamura

BVFUNC_5, miz file
Propositional Calculus for Boolean Valued Functions, I
by Shunichi Kobayashi and Yatsuka Nakamura

BVFUNC_6, miz file
Propositional Calculus for Boolean Valued Functions, II
by Shunichi Kobayashi and Yatsuka Nakamura

BVFUNC_7, miz file
Propositional Calculus For Boolean Valued Functions, III
by Shunichi Kobayashi

BVFUNC_8, miz file
Propositional Calculus For Boolean Valued Functions, IV
by Shunichi Kobayashi

BVFUNC_9, miz file
Propositional Calculus for Boolean Valued Functions, { V }
by Shunichi Kobayashi

A Sequent Calculus for First-Order Logic
by Patrick Braselmann and Peter Koepke

CALCUL_2, miz file
Consequences of the Sequent Calculus
by Patrick Braselmann and Peter Koepke

CANTOR_1, miz file
The Cantor Set
by Alexander Yu. Shibakov and Andrzej Trybulec

CARD_1, miz file
Cardinal Numbers
by Grzegorz Bancerek

CARD_2, miz file
Cardinal Arithmetics
by Grzegorz Bancerek

CARD_3, miz file
K\"onig's Theorem
by Grzegorz Bancerek

CARD_4, miz file
Countable Sets and Hessenberg's Theorem
by Grzegorz Bancerek

CARD_5, miz file
On Powers of Cardinals
by Grzegorz Bancerek

CARD_FIL, miz file
Basic facts about inaccessible and measurable cardinals
by Josef Urban

CARD_FIN, miz file
Cardinal Numbers and Finite Sets
by Karol P\c{a}k

CARD_LAR, miz file
Mahlo and inaccessible cardinals
by Josef Urban

CAT_1, miz file
Introduction to Categories and Functors
by Czes{\l}aw Byli\'nski

CAT_2, miz file
Subcategories and Products of Categories
by Czes{\l}aw Byli\'nski

CAT_3, miz file
Products and Coproducts in Categories
by Czes{\l}aw Byli\'nski

CAT_4, miz file
Cartesian Categories
by Czes{\l}aw Byli\'nski

CAT_5, miz file
Categorial Categories and Slice Categories
by Grzegorz Bancerek

CATALAN1, miz file
Catalan Numbers
by Dorota Cz\c{e}stochowska and Adam Grabowski

CATALG_1, miz file
Algebra of Morphisms
by Grzegorz Bancerek

CFCONT_1, miz file
Property of Complex Sequence and Continuity of Complex Function
by Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama

CFUNCDOM, miz file
Complex Valued Function's Space
by Noboru Endou

CFUNCT_1, miz file
Property of Complex Functions
by Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama

CHAIN_1, miz file
Chains on a Grating in Euclidean Space
by Freek Wiedijk

CIRCCMB2, miz file
Combining of Multi Cell Circuits
by Grzegorz Bancerek , Shin'nosuke Yamaguchi and Yasunari Shidama

CIRCCMB3, miz file
Preliminaries to Automatic Generation of Mizar Documentation for Circuits
by Grzegorz Bancerek and Adam Naumowicz

CIRCCOMB, miz file
Combining of Circuits
by Yatsuka Nakamura and Grzegorz Bancerek

CIRCLED1, miz file
Circled Sets, Circled Hull, and Circled Family
by Fahui Zhai , Jianbing Cao and Xiquan Liang

CIRCTRM1, miz file
Circuit Generated by Terms and Circuit Calculating Terms
by Grzegorz Bancerek

CIRCUIT1, miz file
Introduction to Circuits, I
by Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec and Pauline N. Kawamo

CIRCUIT2, miz file
Introduction to Circuits, II
by Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec and Pauline N. Kawamo

CLASSES1, miz file
Tarski's Classes and Ranks
by Grzegorz Bancerek

CLASSES2, miz file
Universal Classes
by Bogdan Nowak and Grzegorz Bancerek

CLOPBAN1, miz file
Complex {B}anach Space of Bounded Linear Operators
by Noboru Endou

CLOPBAN2, miz file
Banach Algebra of Bounded Complex Linear Operators
by Noboru Endou

CLOPBAN3, miz file
Series on Complex {B}anach Algebra
by Noboru Endou

CLOPBAN4, miz file
Exponential Function on Complex {B}anach Algebra
by Noboru Endou

CLOSURE1, miz file
On the Many Sorted Closure Operator and the Many Sorted Closure
System

CLOSURE2, miz file
On the Closure Operator and the Closure System of Many Sorted Sets
by Artur Korni{\l}owicz

CLOSURE3, miz file
Algebraic Operation on Subsets of Many Sorted Sets
by Agnieszka Julia Marasik

CLVECT_1, miz file
Complex Linear Space and Complex Normed Space
by Noboru Endou

CLVECT_2, miz file
Convergent Sequences in Complex Unitary Space
by Noboru Endou

CLVECT_3, miz file
Cauchy Sequence of Complex Unitary Space
by Yasumasa Suzuki and Noboru Endou

COH_SP, miz file
Coherent Space
by Jaros{\l}aw Kotowicz and Konrad Raczkowski

COHSP_1, miz file
Continuous, Stable, and Linear Maps of Coherence Spaces
by Grzegorz Bancerek

COLLSP, miz file
The Collinearity Structure
by Wojciech Skaba

COMMACAT, miz file
Comma Category
by Grzegorz Bancerek and Agata Darmochwa\l

COMPLEX1, miz file
The Complex Numbers
by Czes{\l}aw Byli\'nski

COMPLEX2, miz file
Inner Products and Angles of Complex Numbers
by Wenpai Chang, Yatsuka Nakamura and Piotr Rudnicki

COMPLFLD, miz file
The Field of Complex Numbers
by Anna Justyna Milewska

COMPLSP1, miz file
Complex Spaces
by Czes{\l}aw Byli\'nski and Andrzej Trybulec

COMPLSP2, miz file
The Inner Product and Conjugate of Finite Sequences of Complex Numbers
by Wenpai Chang , Hiroshi Yamazaki and Yatsuka Nakamura

COMPTRIG, miz file
Trigonometric Form of Complex Numbers
by Robert Milewski

COMPTS_1, miz file
Compact Spaces
by Agata Darmochwa{\l}

COMPUT_1, miz file
The set of primitive recursive functions
by Grzegorz Bancerek and Piotr Rudnicki

COMSEQ_1, miz file
Complex Sequences
by Agnieszka Banachowicz and Anna Winnicka

COMSEQ_2, miz file
Conjugate Sequences, Bounded Complex Sequences and Convergent
Complex Sequences

COMSEQ_3, miz file
Convergence and the Limit of Complex Sequences. Series
by Yasunari Shidama and Artur Korni{\l}owicz

CONAFFM, miz file
Metric-Affine Configurations in Metric Affine Planes - Part I
by Jolanta \'Swierzy\'nska and Bogdan \'Swierzy\'nski

CONLAT_1, miz file
Introduction to Concept Lattices
by Christoph Schwarzweller

CONLAT_2, miz file
A Characterization of Concept Lattices; Dual Concept Lattices
by Christoph Schwarzweller

CONMETR, miz file
Metric-Affine Configurations in Metric Affine Planes - Part II
by Jolanta \'Swierzy\'nska and Bogdan \'Swierzy\'nski

CONMETR1, miz file
Shear Theorems and Their Role in Affine Geometry
by Jolanta \'Swierzy\'nska and Bogdan \'Swierzy\'nski

CONNSP_1, miz file
Connected Spaces
by Beata Padlewska

CONNSP_2, miz file
Locally Connected Spaces
by Beata Padlewska

CONNSP_3, miz file
Components and Unions of Components
by Yatsuka Nakamura and Andrzej Trybulec

CONVEX1, miz file
Convex Sets and Convex Combinations
by Noboru Endou , Takashi Mitsuishi and Yasunari Shidama

CONVEX2, miz file
Some Properties for Convex Combinations
by Noboru Endou , Yasumasa Suzuki and Yasunari Shidama

CONVEX3, miz file
Convex Hull, Set of Convex Combinations and Convex Cone
by Noboru Endou and Yasunari Shidama

CONVFUN1, miz file
Definition of Convex Function and {J}ensen's Inequality
by Grigory E. Ivanov

CQC_LANG, miz file
A Classical First Order Language
by Czes{\l}aw Byli\'nski

CQC_SIM1, miz file
Similarity of Formulae
by Agata Darmochwa{\l} and Andrzej Trybulec

CQC_THE1, miz file
A First-Order Predicate Calculus.
Axiomatics, the Consequence Operation and a Concept of Proof

CQC_THE2, miz file
Calculus of Quantifiers. Deduction Theorem
by Agata Darmochwa\l

CQC_THE3, miz file
Logical Equivalence of Formulae
by Oleg Okhotnikov

CSSPACE, miz file
Complex Linear Space of Complex Sequences
by Noboru Endou

CSSPACE2, miz file
Hilbert Space of Complex Sequences
by Noboru Endou

CSSPACE3, miz file
Banach Space of Absolute Summable Complex Sequences
by Noboru Endou

CSSPACE4, miz file
Complex Banach Space of Bounded Complex Sequences
by Noboru Endou

On the Decomposition of the Continuity
by Marian Przemski

DICKSON, miz file
Dickson's lemma
by Gilbert Lee and Piotr Rudnicki

DIRAF, miz file
Ordered Affine Spaces Defined in Terms of Directed Parallelity - part I
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

DIRORT, miz file
Oriented Metric-Affine Plane - Part II
by Jaros{\l}aw Zajkowski

DOMAIN_1, miz file
Domains and Their Cartesian Products
by Andrzej Trybulec

DTCONSTR, miz file
On Defining Functions on Trees
by Grzegorz Bancerek and Piotr Rudnicki

DYNKIN, miz file
Dynkin's Lemma in Measure Theory
by Franz Merkl

Definitions of Petri Net - Part II
by Waldemar Korczy\'nski

ENDALG, miz file
On the Monoid of Endomorphisms of Universal Algebra \& Many
Sorted Algebra

ENS_1, miz file
Category Ens
by Czes{\l}aw Byli\'nski

ENUMSET1, miz file
Enumerated Sets
by Andrzej Trybulec

EQREL_1, miz file
Equivalence Relations and Classes of Abstraction
by Konrad Raczkowski and Pawe{\l} Sadowski

EQUATION, miz file
Equations in Many Sorted Algebras
by Artur Korni{\l}owicz

EUCLID, miz file
The Euclidean Space
by Agata Darmochwa{\l}

EUCLID_2, miz file
The Inner Product of Finite Sequences and of Points of $n$-dimensional
Topological Space

EUCLID_3, miz file
Angle and Triangle in {E}uclidian Topological Space
by Akihiro Kubo and Yatsuka Nakamura

EUCLID_4, miz file
Lines in $n$-Dimensional Euclidean Spaces
by Akihiro Kubo

EUCLID_5, miz file
Cross Products and Tripple Vector Products in 3-dimensional Euclidian Space
by Kanchun, Hiroshi Yamazakiand Yatsuka Nakamura

EUCLIDLP, miz file
Lines on Planes in $n$-Dimensional Euclidean Spaces
by Akihiro Kubo

EUCLMETR, miz file
Fundamental Types of Metric Affine Spaces
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

EULER_1, miz file
Euler's Function
by Yoshinori Fujisawa and Yasushi Fuwa

EULER_2, miz file
Euler's {T}heorem and Small {F}ermat's Theorem
by Yoshinori Fujisawa , Yasushi Fuwa and Hidetaka Shimizu

EXTENS_1, miz file
Extensions of Mappings on Generator Set
by Artur Korni{\l}owicz

EXTREAL1, miz file
Basic Properties of Extended Real Numbers
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama

EXTREAL2, miz file
Some Properties of Extended Real Numbers Operations: absolute
value, min and max

Full Adder Circuit. Part { I }
by Grzegorz Bancerek and Yatsuka Nakamura

FACIRC_2, miz file
Full Adder Circuit. Part { II }
by Grzegorz Bancerek , Shin'nosuke Yamaguchi and Katsumi Wasaki

FCONT_1, miz file
Real Function Continuity
by Konrad Raczkowski and Pawe{\l} Sadowski

FCONT_2, miz file
Real Function Uniform Continuity
by Jaros{\l}aw Kotowicz and Konrad Raczkowski

FCONT_3, miz file
Monotonic and Continuous Real Function
by Jaros{\l}aw Kotowicz

FDIFF_1, miz file
Real Function Differentiability
by Konrad Raczkowski and Pawe{\l} Sadowski

FDIFF_2, miz file
Real Function Differentiability - Part II
by Jaros{\l}aw Kotowicz and Konrad Raczkowski

FDIFF_3, miz file
Real Function One-Side Differantiability
by Ewa Burakowska and Beata Madras

FDIFF_4, miz file
Several Differentiable Formulas of Special Functions
by Yan Zhang and Xiquan Liang

FDIFF_5, miz file
Some Differentiable Formulas of Special Functions
by Jianbing Cao , Fahui Zhai and Xiquan Liang

FDIFF_6, miz file
Several Differentiable Formulas of Special Functions -- Part {II}
by Yan Zhang , Bo Li and Xiquan Liang

FDIFF_7, miz file
Several Differentiation Formulas of Special Functions -- Part {III}
by Bo Li , Yan Zhang and Xiquan Liang

FF_SIEC, miz file
Definitions of Petri Net - Part I
by Waldemar Korczy\'nski

FIB_FUSC, miz file
Two Programs for {\bf SCM}. Part II - Proofs
by Grzegorz Bancerek and Piotr Rudnicki

FIB_NUM, miz file
Fibonacci Numbers
by Robert M. Solovay

FIB_NUM2, miz file
Some Properties of {F}ibonacci Numbers
by Magdalena Jastrz\c{e}bska and Adam Grabowski

FIB_NUM3, miz file
Lucas Numbers and Generalized {F}ibonacci Numbers
by Piotr Wojtecki and Adam Grabowski

FILEREC1, miz file
A Theory of Sequential Files
by Hirofumi Fukura and Yatsuka Nakamura

FILTER_0, miz file
Filters - Part I. Implicative Lattices
by Grzegorz Bancerek

FILTER_1, miz file
Filters - Part II. Quotient Lattices Modulo Filters and
Direct Product of Two Lattices

FILTER_2, miz file
Ideals
by Grzegorz Bancerek

FIN_TOPO, miz file
Finite Topological Spaces. Finite Topology Concepts and Neighbourhoods
by Hiroshi Imura and Masayoshi Eguchi

FINSEQ_1, miz file
Segments of Natural Numbers and Finite Sequences
by Grzegorz Bancerek and Krzysztof Hryniewiecki

FINSEQ_2, miz file
Finite Sequences and Tuples of Elements of a Non-empty Sets
by Czes{\l}aw Byli\'nski

FINSEQ_3, miz file
Non-contiguous Substrings and One-to-one Finite Sequences
by Wojciech A. Trybulec

FINSEQ_4, miz file
Pigeon Hole Principle
by Wojciech A. Trybulec

FINSEQ_5, miz file
Some Properties of Restrictions of Finite Sequences
by Czes\law Byli\'nski

FINSEQ_6, miz file
On the Decomposition of Finite Sequences
by Andrzej Trybulec

FINSEQ_7, miz file
On Replace Function and Swap Function for Finite Sequences
by Hiroshi Yamazaki , Yoshinori Fujisawa and Yatsuka Nakamura

FINSEQ_8, miz file
Concatenation of Finite Sequences Reducing Overlapping Part and an
Argument of Separators of Sequential Files

FINSEQOP, miz file
Binary Operations Applied to Finite Sequences
by Czes{\l}aw Byli\'nski

FINSET_1, miz file
Finite Sets
by Agata Darmochwa\l

FINSOP_1, miz file
Binary Operations on Finite Sequences
by Wojciech A. Trybulec

FINSUB_1, miz file
Boolean Domains
by Andrzej Trybulec and Agata Darmochwa\l

FINTOPO2, miz file
Formal topological spaces
by Gang Liu , Yasushi Fuwa and Masayoshi Eguchi

FINTOPO3, miz file
Some Set Series in Finite Topological Spaces. {F}undamental Concepts
for Image Processing

FINTOPO4, miz file
Continuous Mappings between Finite and One-Dimensional Finite Topological
Spaces

FINTOPO5, miz file
Homeomorphism between Finite Topological Spaces, Two-Dimensional Lattice
Spaces and a Fixed Point Theorem

FRAENKEL, miz file
Function Domains and Fr{\ae}nkel Operator
by Andrzej Trybulec

FRECHET, miz file
First-countable, Sequential, and { F } rechet Spaces
by Bart{\l}omiej Skorulski

FRECHET2, miz file
The Sequential Closure Operator In Sequential and Frechet Spaces
by Bart{\l}omiej Skorulski

FREEALG, miz file
Free Universal Algebra Construction
by Beata Perkowska

FSCIRC_1, miz file
Full Subtracter Circuit. Part { I }
by Katsumi Wasaki and Noboru Endou

FSCIRC_2, miz file
Full Subtracter Circuit. Part {II}
by Shin'nosuke Yamaguchi , Grzegorz Bancerek and Katsumi Wasaki

FSM_1, miz file
Minimization of finite state machines
by Miroslava Kaloper and Piotr Rudnicki

FSM_2, miz file
On state machines of calculating type
by Hisayoshi Kunimune , Grzegorz Bancerek and Yatsuka Nakamura

FUNCOP_1, miz file
Binary Operations Applied to Functions
by Andrzej Trybulec

FUNCSDOM, miz file
Real Functions Spaces
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

FUNCT_1, miz file
Functions and Their Basic Properties
by Czes{\l}aw Byli\'nski

FUNCT_2, miz file
Functions from a Set to a Set
by Czes{\l}aw Byli\'nski

FUNCT_3, miz file
Basic Functions and Operations on Functions
by Czes{\l}aw Byli\'nski

FUNCT_4, miz file
The Modification of a Function by a Function
and the Iteration of the Composition of a Function

FUNCT_5, miz file
Curried and Uncurried Functions
by Grzegorz Bancerek

FUNCT_6, miz file
Cartesian Product of Functions
by Grzegorz Bancerek

FUNCT_7, miz file
Miscellaneous Facts about Functions
by Grzegorz Bancerek and Andrzej Trybulec

FUNCTOR0, miz file
Functors for Alternative Categories
by Andrzej Trybulec

FUNCTOR1, miz file
Basic Properties of Functor Structures
by Claus Zinn and Wolfgang Jaksch

FUNCTOR2, miz file
Category of Functors between Alternative Categories
by Robert Nieszczerzewski

FUNCTOR3, miz file
The Composition of Functors and Transformations in Alternative
Categories

FUZZY_1, miz file
Concept of Fuzzy Set and Membership Function and Basic
Properties of Fuzzy Set Operation

FUZZY_2, miz file
Basic Properties of Fuzzy Set Operation and Membership Function
by Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama

FUZZY_3, miz file
Concept of Fuzzy Relation and Basic Properties of Its Operation
by Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama

FUZZY_4, miz file
Properties of Fuzzy Relation
by Noboru Endou , Takashi Mitsuishi and Keiji Ohkubo

FVSUM_1, miz file
Sum and Product of Finite Sequences of Elements of a Field
by Katarzyna Zawadzka

Logic Gates and Logical Equivalence of Adders
by Yatsuka Nakamura

GATE_2, miz file
Correctness of Binary Counter Circuits
by Yuguang Yang , Wasaki Katsumi , Yasushi Fuwa and Yatsuka Nakamura

GATE_3, miz file
Correctness of Johnson Counter Circuits
by Yuguang Yang , Wasaki Katsumi , Yasushi Fuwa and Yatsuka Nakamura

GATE_4, miz file
Correctness of a Cyclic Redundancy Check Code Generator
by Yuguang Yang , Katsumi Wasaki , Yasushi Fuwa and Yatsuka Nakamura

GATE_5, miz file
Correctness of the High Speed Array Multiplier Circuits
by Hiroshi Yamazaki and Katsumi Wasaki

GCD_1, miz file
The correctness of the Generic Algorithms of Brown and Henrici
concerning Addition and Multiplication in Fraction Fields

GENEALG1, miz file
Basic Properties of Genetic Algorithm
by Akihiko Uchibori and Noboru Endou

GEOMTRAP, miz file
A Construction of Analytical Ordered Trapezium Spaces
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

GFACIRC1, miz file
Generalized Full Adder Circuits (GFAs). {P}art {I}
by Shin'nosuke Yamaguchi , Katsumi Wasaki and Nobuhiro Shimoi

GLIB_000, miz file
Alternative Graph Structures
by Gilbert Lee and Piotr Rudnicki

GLIB_001, miz file
Walks in a Graph
by Gilbert Lee

GLIB_002, miz file
Trees: Connected, Acyclic Graphs
by Gilbert Lee

GLIB_003, miz file
Weighted and Labeled Graphs
by Gilbert Lee

GLIB_004, miz file
Proof of Dijkstra's Shortest Path Algorithm & Prim's Minimum Spanning
Tree Algorithm

GLIB_005, miz file
Proof of Ford/Fulkerson's Maximum Network Flow Algorithm
by Gilbert Lee

GOBOARD1, miz file
Introduction to Go-Board - Part I. Basic Notations
by Jaros{\l}aw Kotowicz and Yatsuka Nakamura

GOBOARD2, miz file
Introduction to Go-Board - Part II.
Go-Board Determined by Finite Sequence of point from ${\calE}^2_{\rm T}$

GOBOARD3, miz file
Properties of Go-Board - Part III
by Jaros{\l}aw Kotowicz and Yatsuka Nakamura

GOBOARD4, miz file
Go-Board Theorem
by Jaros{\l}aw Kotowicz and Yatsuka Nakamura

GOBOARD5, miz file
Decomposing a Go Board into Cells
by Yatsuka Nakamura and Andrzej Trybulec

GOBOARD6, miz file
On the Geometry of a Go-board
by Andrzej Trybulec

GOBOARD7, miz file
On the Go Board of a Standard Special Circular Sequence
by Andrzej Trybulec

GOBOARD8, miz file
More on Segments on a Go Board
by Andrzej Trybulec

GOBOARD9, miz file
Left and Right Component of the Complement of a Special Closed Curve
by Andrzej Trybulec

GOBRD10, miz file
Adjacency Concept for Pairs of Natural Numbers
by Yatsuka Nakamura and Andrzej Trybulec

GOBRD11, miz file
Some Topological Properties of Cells in $R^2$
by Yatsuka Nakamura and Andrzej Trybulec

GOBRD12, miz file
The First Part of Jordan's Theorem for Special Polygons
by Yatsuka Nakamura and Andrzej Trybulec

GOBRD13, miz file
Some Properties of Cells on Go Board
by Czes{\l}aw Byli\'nski

GOBRD14, miz file
Properties of Left-, and Right Components
by Artur Korni{\l}owicz

GOEDELCP, miz file
G{\"o}del's Completeness Theorem
by Patrick Braselmann and Peter Koepke

GR_CY_1, miz file
Cyclic Groups and Some of Their Properties - Part I
by Dariusz Surowik

GR_CY_2, miz file
Isomorphisms of Cyclic Groups. Some Properties of Cyclic Groups
by Dariusz Surowik

GRAPH_1, miz file
Graphs
by Krzysztof Hryniewiecki

GRAPH_2, miz file
Vertex sequences induced by chains
by Yatsuka Nakamura and Piotr Rudnicki

GRAPH_3, miz file
Euler circuits and paths
by Yatsuka Nakamura and Piotr Rudnicki

GRAPH_4, miz file
Oriented Simple Chains Included in Oriented Chains
by Yatsuka Nakamura and Piotr Rudnicki

GRAPH_5, miz file
The Underlying Principle of {D}ijkstra's Shortest Path Algorithm
by Jingchao Chen and Yatsuka Nakamura

GRAPHSP, miz file
Dijkstra's Shortest Path Algorithm
by Jing-Chao Chen

GRCAT_1, miz file
Categories of Groups
by Michal Muzalewski

GRFUNC_1, miz file
Graphs of Functions
by Czes{\l}aw Byli\'nski

GROEB_1, miz file
Characterization and Existence of {G}r\"obner Bases
by Christoph Schwarzweller

GROEB_2, miz file
Construction of {G}r\"obner bases. S-Polynomials and Standard
Representations

GROEB_3, miz file
Construction of {G}r\"obner Bases: Avoiding S-Polynomials -- Buchberger's
First Criterium

GROUP_1, miz file
Groups
by Wojciech A. Trybulec

GROUP_2, miz file
Subgroup and Cosets of Subgroups. Lagrange theorem
by Wojciech A. Trybulec

GROUP_3, miz file
Classes of Conjugation. Normal Subgroups
by Wojciech A. Trybulec

GROUP_4, miz file
Lattice of Subgroups of a Group. Frattini Subgroup
by Wojciech A. Trybulec

GROUP_5, miz file
Commutator and Center of a Group
by Wojciech A. Trybulec

GROUP_6, miz file
Homomorphisms and Isomorphisms of Groups. Quotient Group
by Wojciech A. Trybulec and Micha{\l} J. Trybulec

GROUP_7, miz file
The Product of the Families of the Groups
by Artur Korni{\l}owicz

GROUP_8, miz file
Properties of Groups
by Gijs Geleijnse and Grzegorz Bancerek

GRSOLV_1, miz file
Solvable Groups
by Katarzyna Zawadzka

Hahn Banach Theorem
by Bogdan Nowak and Andrzej Trybulec

HAHNBAN1, miz file
Hahn Banach Theorem in the Vector Space over the Field of
Complex Numbers

HALLMAR1, miz file
The {H}all {M}arriage {T}heorem
by Ewa Romanowicz and Adam Grabowski

HAUSDORF, miz file
On the {H}ausdorff Distance Between Compact Subsets
by Adam Grabowski

HEINE, miz file
Heine--Borel's Covering Theorem
by Agata Darmochwa{\l} and Yatsuka Nakamura

HENMODEL, miz file
Equivalences of Inconsistency and {H}enkin Models
by Patrick Braselmann and Peter Koepke

HERMITAN, miz file
Hermitan Functionals. {C}anonical Construction of Scalar Product in
Quotient Vector Space

HESSENBE, miz file
Hessenberg Theorem
by Eugeniusz Kusak and Wojciech Leo\'nczuk

HEYTING1, miz file
Algebra of Normal Forms Is a Heyting Algebra
by Andrzej Trybulec

HEYTING2, miz file
Lattice of Substitutions Is a Heyting Algebra
by Adam Grabowski

HEYTING3, miz file
The Incompleteness of the Lattice of Substitutions
by Adam Grabowski

HIDDEN, miz file
Built-in Concepts
by Andrzej Trybulec

HILBASIS, miz file
Hilbert Basis Theorem
by Jonathan Backer and Piotr Rudnicki

HILBERT1, miz file
Hilbert Positive Propositional Calculus
by Adam Grabowski

HILBERT2, miz file
Defining by structural induction in the positive propositional language
by Andrzej Trybulec

HILBERT3, miz file
The canonical formulae
by Andrzej Trybulec

HOLDER_1, miz file
H\"older's Inequality and {M}inkowski's Inequality
by Yasumasa Suzuki

HOMOTHET, miz file
Homotheties and Shears in Affine Planes
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

Algebraic group on Fixed-length bit integer and its adaptation
to {IDEA} Cryptography

IDEAL_1, miz file
Ring Ideals
by Jonathan Backer , Piotr Rudnicki and Christoph Schwarzweller

INCPROJ, miz file
Incidence Projective Spaces
by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski

INCSP_1, miz file
Axioms of Incidency
by Wojciech A. Trybulec

INDEX_1, miz file
Indexed Category
by Grzegorz Bancerek

INSTALG1, miz file
Institution of Many-sorted Algebras, Part { I } : Signature Reduct
of an Algebra

INT_1, miz file
Integers
by Micha{\l} J. Trybulec

INT_2, miz file
The Divisibility of Integers and Integer Relatively Primes
by Rafa{\l} Kwiatek and Grzegorz Zwara

INT_3, miz file
The Ring of Integers, Euclidean Rings and Modulo Integers
by Christoph Schwarzweller

INTEGRA1, miz file
The Definition of Riemann Definite Integral and some Related Lemmas
by Noboru Endou and Artur Korni{\l}owicz

INTEGRA2, miz file
Scalar Multiple of Riemann Definite Integral
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama

INTEGRA3, miz file
Darboux's Theorem
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama

INTEGRA4, miz file
Integrability of Bounded Total Functions
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama

INTEGRA5, miz file
Definition of Integrability for Partial Functions from REAL to
REAL and Integrability for Continuous Functions

INTPRO_1, miz file
Intuitionistic Propositional Calculus in the Extended Framework with Modal
Operator, Part I

IRRAT_1, miz file
Irrationality of e
by Freek Wiedijk

ISOCAT_1, miz file
Isomorphisms of Categories
by Andrzej Trybulec

ISOCAT_2, miz file
Some Isomorphisms Between Functor Categories
by Andrzej Trybulec

ISOMICHI, miz file
The Properties of Supercondensed Sets, Subcondensed Sets and Condensed Sets
by Magdalena Jastrz\c{e}bska and Adam Grabowski

Miscellaneous { I }
by Andrzej Trybulec

JGRAPH_1, miz file
Graph Theoretical Properties of Arcs in the Plane and Fashoda
Meet Theorem

JGRAPH_2, miz file
On Outside Fashoda Meet Theorem
by Yatsuka Nakamura

JGRAPH_3, miz file
On the Simple Closed Curve Property of the Circle and the
Fashoda Meet Theorem for It

JGRAPH_4, miz file
Fan Homeomorphisms in the Plane
by Yatsuka Nakamura

JGRAPH_5, miz file
General {F}ashoda {M}eet {T}heorem for Unit Circle
by Yatsuka Nakamura

JGRAPH_6, miz file
General {F}ashoda Meet Theorem for Unit Circle and Square
by Yatsuka Nakamura

JGRAPH_7, miz file
Fashoda Meet Theorem for Rectangles
by Yatsuka Nakamura and Andrzej Trybulec

JGRAPH_8, miz file
The {F}ashoda Meet Theorem for Continuous Mappings
by Yatsuka Nakamura , Andrzej Trybulec and Artur Korni{\l}owicz

JORDAN, miz file
Jordan's Curve Theorem
by Artur Korni{\l}owicz

JORDAN1, miz file
The Jordan's Property for Certain Subsets of the Plane
by Yatsuka Nakamura and Jaros{\l}aw Kotowicz

JORDAN10, miz file
Properties of the External Approximation of Jordan's Curve
by Artur Korni{\l}owicz

JORDAN11, miz file
Preparing the Internal Approximations of Simple Closed Curves
by Andrzej Trybulec

JORDAN12, miz file
On the General Position of Special Polygons
by Mariusz Giero

JORDAN13, miz file
Introducing Spans
by Andrzej Trybulec

JORDAN14, miz file
Properties of the Internal Approximation of {J}ordan's Curve
by Robert Milewski

JORDAN15, miz file
Properties of the Upper and Lower Sequence on the Cage
by Robert Milewski

JORDAN16, miz file
On the Decomposition of a Simple Closed Curve into Two Arcs
by Andrzej Trybulec and Yatsuka Nakamura

JORDAN17, miz file
The Ordering of Points on a Curve, Part {III}
by Artur Korni{\l}owicz

JORDAN18, miz file
The Ordering of Points on a Curve, Part {IV}
by Artur Korni{\l}owicz

JORDAN19, miz file
On the Upper and Lower Approximations of the Curve
by Robert Milewski

JORDAN1A, miz file
Gauges and Cages
by Artur Korni{\l}owicz, Robert Milewski, Adam Naumowicz and

JORDAN1B, miz file
Some Properties of Cells and Arcs
by Robert Milewski , Andrzej Trybulec , Artur Korni{\l}owicz

JORDAN1C, miz file
Some Properties of Cells and Gauges
by Adam Grabowski , Artur Korni{\l}owicz and Andrzej Trybulec

JORDAN1D, miz file
Gauges and Cages. { P } art { II }
by Artur Korni{\l}owicz and Robert Milewski

JORDAN1E, miz file
Upper and Lower Sequence of a Cage
by Robert Milewski

JORDAN1F, miz file
Some Remarks on Finite Sequences on Go-boards
by Adam Naumowicz

JORDAN1G, miz file
Upper and Lower Sequence on the Cage. Part II
by Robert Milewski

JORDAN1H, miz file
More on External Approximation of a Continuum
by Andrzej Trybulec

JORDAN1I, miz file
Some Remarks on Clockwise Oriented Sequences on Go-boards
by Adam Naumowicz and Robert Milewski

JORDAN1J, miz file
Upper and Lower Sequence on the Cage, Upper and Lower Arcs
by Robert Milewski

JORDAN1K, miz file
On the Minimal Distance Between Set in {E}uclidean Space
by Andrzej Trybulec

JORDAN20, miz file
Behaviour of an Arc Crossing a Line
by Yatsuka Nakamura

JORDAN21, miz file
On Some Points of a Simple Closed Curve
by Artur Korni{\l}owicz

JORDAN22, miz file
On Some Points of a Simple Closed Curve. {P}art {II}
by Artur Korni{\l}owicz and Adam Grabowski

JORDAN23, miz file
Subsequences of Almost, Weakly and Poorly One-to-one Finite Sequences
by Robert Milewski

JORDAN24, miz file
Homeomorphisms of {J}ordan Curves
by Adam Naumowicz and Grzegorz Bancerek

JORDAN2B, miz file
Projections in n-Dimensional Euclidean Space to Each Coordinates
by Roman Matuszewski and Yatsuka Nakamura

JORDAN2C, miz file
Bounded Domains and Unbounded Domains
by Yatsuka Nakamura , Andrzej Trybulec and Czeslaw Bylinski

JORDAN3, miz file
Reconstructions of Special Sequences
by Yatsuka Nakamura and Roman Matuszewski

JORDAN4, miz file
Subsequences of Standard Special Circular Sequences in $ { \cal E
} ^2_ { \rm T } $

JORDAN5A, miz file
Some Properties of Real Maps
by Adam Grabowski and Yatsuka Nakamura

JORDAN5B, miz file
The Ordering of Points on a Curve, Part { I }
by Adam Grabowski and Yatsuka Nakamura

JORDAN5C, miz file
The Ordering of Points on a Curve, Part { II }
by Adam Grabowski and Yatsuka Nakamura

JORDAN5D, miz file
Bounding Boxes for Special Sequences in ${\calE}^2$
by Yatsuka Nakamura and Adam Grabowski

JORDAN6, miz file
A Decomposition of Simple Closed Curves and an Order of Their Points
by Yatsuka Nakamura and Andrzej Trybulec

JORDAN7, miz file
On a Dividing Function of the Simple Closed Curve into Segments
by Yatsuka Nakamura

JORDAN8, miz file
Gauges
by Czes\law Byli\'nski

JORDAN9, miz file
Cages, external aproximation of Jordan's curve
by Czes{\l}aw Byli\'nski and Mariusz \.Zynel

JORDAN_A, miz file
On the Segmentation of a Simple Closed Curve
by Andrzej Trybulec

Fix-points in complete lattices
by Piotr Rudnicki and Andrzej Trybulec

KURATO_1, miz file
On the {K}uratowski Closure-Complement Problem
by Lilla Krystyna Bagi\'nska and Adam Grabowski

KURATO_2, miz file
On the {K}uratowski Limit Operators
by Adam Grabowski

The de l'Hospital Theorem
by Ma{\l}gorzata Korolkiewicz

LANG1, miz file
Context-Free Grammar - Part 1
by Patricia L. Carlson and Grzegorz Bancerek

LATSUBGR, miz file
On the Lattice of Subgroups of a Group
by Janusz Ganczarski

LATSUM_1, miz file
The Operation of Addition of Relational Structures
by Katarzyna Romanowicz and Adam Grabowski

LATTICE2, miz file
Finite Join and Finite Meet, and Dual Lattices
by Andrzej Trybulec

LATTICE3, miz file
Complete Lattices
by Grzegorz Bancerek

LATTICE4, miz file
Homomorphisms of Lattices \\ Finite Join and Finite Meet
by Jolanta Kamie\'nska and Jaros\l aw Stanis\l aw Walijewski

LATTICE5, miz file
J\'onsson Theorem
by Jaros{\l}aw Gryko

LATTICE6, miz file
Noetherian Lattices
by Christoph Schwarzweller

LATTICE7, miz file
Representation Theorem For Finite Distributive Lattices
by Marek Dudzicz

LATTICE8, miz file
J\'onsson Theorem about Representation of Modular Lattices
by Mariusz {\L}api\'nski

LATTICES, miz file
Introduction to Lattice Theory
by Stanis{\l}aw \.Zukowski

LFUZZY_0, miz file
Lattice of Fuzzy Sets
by Takashi Mitsuishi and Grzegorz Bancerek

LFUZZY_1, miz file
Transitive Closure of Fuzzy Relations
by Takashi Mitsuishi and Grzegorz Bancerek

LIMFUNC1, miz file
The Limit of a Real Function at Infinity. Halflines.
Real Sequence Divergent to Infinity

LIMFUNC2, miz file
One-Side Limits of a Real Function at a Point
by Jaros{\l}aw Kotowicz

LIMFUNC3, miz file
The Limit of a Real Function at a Point
by Jaros{\l}aw Kotowicz

LIMFUNC4, miz file
The Limit of a Composition of Real Functions
by Jaros{\l}aw Kotowicz

LMOD_5, miz file
Linear Independence in Left Module over Domain
by Micha{\l} Muzalewski and Wojciech Skaba

LMOD_6, miz file
Submodules
by Micha{\l} Muzalewski

LMOD_7, miz file
Domains of Submodules, Join and Meet of Finite Sequences of Submodules
and Quotient Modules

LOPBAN_1, miz file
Banach Space of Bounded Linear Operators
by Yasunari Shidama

LOPBAN_2, miz file
The {B}anach Algebra of Bounded Linear Operators
by Yasunari Shidama

LOPBAN_3, miz file
The Series on {B}anach Algebra
by Yasunari Shidama

LOPBAN_4, miz file
The Exponential Function on {B}anach Algebra
by Yasunari Shidama

LOPCLSET, miz file
Representation Theorem for Boolean Algebras
by Jaros{\l}aw Stanis{\l}aw Walijewski

LP_SPACE, miz file
The Banach Space $l^p$
by Yasumasa Suzuki

LUKASI_1, miz file
Propositional Calculus
by Grzegorz Bancerek, Agata Darmochwa\l and Andrzej Trybulec

Many-Argument Relations
by Edmund Woronowicz

MATHMORP, miz file
Preliminaries to Mathematical Morphology and Its Properties
by Yuzhong Ding and Xiquan Liang

MATRIX_1, miz file
Matrices. Abelian Group of Matrices
by Katarzyna Jankowska

MATRIX_2, miz file
Transpose Matrices and Groups of Permutations
by Katarzyna Jankowska

MATRIX_3, miz file
The Product of Matrices of Elements of a Field and Determinants
by Katarzyna Zawadzka

MATRIX_4, miz file
Calculation of Matrices of Field Elements. Part {I}
by Yatsuka Nakamura and Hiroshi Yamazaki

MATRIX_5, miz file
A Theory of Matrices of Complex Elements
by Wenpai Chang , Hiroshi Yamazaki and Yatsuka Nakamura

MATRIX_6, miz file
Some Properties Of Some Special Matrices
by Xiaopeng Yue , Xiquan Liang and Zhongpin Sun

MATRIX_7, miz file
Determinant of Some Matrices of Field Elements
by Yatsuka Nakamura

MATRIX_8, miz file
Some Properties Of Some Special Matrices, Part {II}
by Xiaopeng Yue , Dahai Hu , Xiquan Liang and Zhongpin Sun

MATRIX_9, miz file
On the Permanent of a Matrix
by Ewa Romanowicz and Adam Grabowski

MATRIXC1, miz file
The Inner Product and Conjugate of Matrix of Complex Numbers
by Wenpai Chang , Hiroshi Yamazaki and Yatsuka Nakamura

MATRIXR1, miz file
A Theory of Matrices of Real Elements
by Yatsuka Nakamura , Nobuyuki Tamaura and Wenpai Chang

MATRLIN, miz file
Associated Matrix of Linear Map
by Robert Milewski

MBOOLEAN, miz file
Definitions and Basic Properties of Boolean & Union of Many
Sorted Sets

MCART_1, miz file
Tuples, Projections and Cartesian Products
by Andrzej Trybulec

MCART_2, miz file
N-Tuples and Cartesian Products for n=5
by Micha{\l} Muzalewski and Wojciech Skaba

MCART_3, miz file
Tuples and Cartesian Products for n=6
by Michal Muzalewski and Wojciech Skaba

MCART_4, miz file
Tuples and Cartesian Products for n=7
by Michal Muzalewski and Wojciech Skaba

MCART_5, miz file
Tuples and Cartesian Products for n=8
by Michal Muzalewski and Wojciech Skaba

MCART_6, miz file
Tuples and Cartesian Products for n=9
by Michal Muzalewski and Wojciech Skaba

MEASURE1, miz file
The $\sigma$-additive Measure Theory
by J\'ozef Bia{\l}as

MEASURE2, miz file
Several Properties of the $\sigma$-additive Measure. Discrete categories
by J\'ozef Bia{\l}as

MEASURE3, miz file
Completeness of the $\sigma$-Additive Measure. Measure Theory
by J\'ozef Bia{\l}as

MEASURE4, miz file
Properties of Caratheodor's Measure
by J\'ozef Bia{\l}as

MEASURE5, miz file
Properties of the Intervals of Real Numbers
by J\'ozef Bia{\l}as

MEASURE6, miz file
Some Properties of the Intervals
by J\'ozef Bia\las

MEASURE7, miz file
The One-Dimensional Lebesgue Measure As an Example of a
Formalization in the Mizar Language of the Classical Definition

MEMBERED, miz file
On the Sets Inhabited by Numbers
by Andrzej Trybulec

MESFUNC1, miz file
Definitions and Basic Properties of Measurable Functions
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama

MESFUNC2, miz file
Measurability of Extended Real Valued Functions
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama

MESFUNC3, miz file
Lebesgue Integral of Simple Valued Function
by Yasunari Shidama and Noboru Endou

MESFUNC4, miz file
Linearity of {L}ebesgue Integral of Simple Valued Function
by Noboru Endou and Yasunari Shidama

MESFUNC5, miz file
Integral of Measurable Function
by Noboru Endou and Yasunari Shidama

METRIC_1, miz file
Metric Spaces
by Stanis{\l}awa Kanas, Adam Lecko and Mariusz Startek

METRIC_2, miz file
On Pseudometric Spaces
by Adam Lecko and Mariusz Startek

METRIC_3, miz file
Metrics in Cartesian Product
by Stanis{\l}awa Kanas and Jan Stankiewicz

METRIC_4, miz file
Metrics in the Cartesian Product - Part II
by Stanis\l awa Kanas and Adam Lecko

METRIC_6, miz file
Sequences in Metric Spaces
by Stanis{\l}awa Kanas and Adam Lecko

MIDSP_1, miz file
Midpoint algebras
by Micha{\l} Muzalewski

MIDSP_2, miz file
Atlas of Midpoint Algebra
by Micha{\l} Muzalewski

MIDSP_3, miz file
Reper Algebras
by Micha{\l} Muzalewski

MOD_1, miz file
Groups, Rings, Left- and Right-Modules
by Micha{\l} Muzalewski and Wojciech Skaba

MOD_2, miz file
Rings and Modules - Part II
by Michal Muzalewski

MOD_3, miz file
Free Modules
by Michal Muzalewski

MOD_4, miz file
Opposite Rings, Modules and their Morphisms
by Micha{\l} Muzalewski

MODAL_1, miz file
Introduction to Modal Propositional Logic
by Alicia de la Cruz

MODCAT_1, miz file
Category of Left Modules
by Micha{\l} Muzalewski

MOEBIUS1, miz file
On the Properties of the {M}\"obius Function
by Magdalena Jastrz\c{e}bska and Adam Grabowski

MONOID_0, miz file
Monoids
by Grzegorz Bancerek

MONOID_1, miz file
Monoid of Multisets and Subsets
by Grzegorz Bancerek

MSAFREE, miz file
Free Many Sorted Universal Algebra
by Beata Perkowska

MSAFREE1, miz file
A Scheme for Extensions of Homomorphisms of Manysorted Algebras
by Andrzej Trybulec

MSAFREE2, miz file
Preliminaries to Circuits, II
by Yatsuka Nakamura , Piotr Rudnicki , Andrzej Trybulec and Pauline N. Kawa

MSAFREE3, miz file
Yet another construction of free algebra
by Grzegorz Bancerek and Artur Korni{\l}owicz

MSALIMIT, miz file
Inverse Limits of Many Sorted Algebras
by Adam Grabowski

MSATERM, miz file
Terms over many sorted universal algebra
by Grzegorz Bancerek

MSINST_1, miz file
Examples of Category Structures
by Adam Grabowski

MSSCYC_1, miz file
The Correspondence Between Monotonic Many Sorted Signatures
and Well-Founded Graphs. {P}art {I}

MSSCYC_2, miz file
The Correspondence Between Monotonic Many Sorted Signatures
and Well-Founded Graphs. {P}art {II}

MSSUBFAM, miz file
Certain Facts about Families of Subsets of Many Sorted Sets
by Artur Korni{\l}owicz

MSSUBLAT, miz file
The Correspondence Between Lattices of Subalgebras of Universal
Algebras and Many Sorted Algebras

MSUALG_1, miz file
Many Sorted Algebras
by Andrzej Trybulec

MSUALG_2, miz file
Subalgebras of a Many Sorted Algebra. Lattice of Subalgebras
by Ewa Burakowska

MSUALG_3, miz file
Homomorphisms of Many Sorted Algebras
by Ma{\l}gorzata Korolkiewicz

MSUALG_4, miz file
Many Sorted Quotient Algebra
by Ma{\l}gorzata Korolkiewicz

MSUALG_5, miz file
Lattice of Congruences in a Many Sorted Algebra
by Robert Milewski

MSUALG_6, miz file
Translations, Endomorphisms, and Stable Equational Theories
by Grzegorz Bancerek

MSUALG_7, miz file
More on the Lattice of Many Sorted Equivalence Relations
by Robert Milewski

MSUALG_8, miz file
More on the Lattice of Congruences in a Many Sorted Algebra
by Robert Milewski

MSUALG_9, miz file
On the Trivial Many Sorted Algebras and Many Sorted Congruences
by Artur Korni\l owicz

MSUHOM_1, miz file
The Correspondence Between Homomorphisms of Universal Algebra &
Many Sorted Algebra

MULTOP_1, miz file
Three-Argument Operations and Four-Argument Operations
by Michal Muzalewski and Wojciech Skaba

The {N}agata-Smirnov Theorem. {P}art {I}
by Karol P\c{a}k

NAGATA_2, miz file
The {N}agata-Smirnov Theorem. {P}art {II}
by Karol P\c{a}k

NAT_1, miz file
The Fundamental Properties of Natural Numbers
by Grzegorz Bancerek

NAT_2, miz file
Natural Numbers
by Robert Milewski

NAT_3, miz file
Fundamental {T}heorem of {A}rithmetic
by Artur Korni{\l}owicz and Piotr Rudnicki

NAT_4, miz file
Pocklington's Theorem and {B}ertrand's Postulate
by Marco Riccardi

NAT_LAT, miz file
The Lattice of Natural Numbers and The Sublattice of it.
The Set of Prime Numbers

NATTRA_1, miz file
Natural Transformations. Discrete Categories
by Andrzej Trybulec

NCFCONT1, miz file
Continuous Functions on Real and Complex Normed Linear Spaces
by Noboru Endou

NCFCONT2, miz file
Uniform Continuity of Functions on Normed Complex Linear Spaces
by Noboru Endou

NDIFF_1, miz file
The Differentiable Functions on Normed Linear Spaces
by Hiroshi Imura , Morishige Kimura and Yasunari Shidama

NDIFF_2, miz file
Differentiable Functions on Normed Linear Spaces. {P}art {II}
by Hiroshi Imura , Yuji Sakai and Yasunari Shidama

NECKLA_2, miz file
The Class of Series-Parallel Graphs, {II}
by Krzysztof Retel

NECKLA_3, miz file
The Class of Series-Parallel Graphs, {III}
by Krzysztof Retel

NECKLACE, miz file
The Class of Series --- Parallel Graphs, {I}
by Krzysztof Retel

NET_1, miz file
Some Elementary Notions of the Theory of Petri Nets
by Waldemar Korczy\'nski

NEWTON, miz file
Factorial and Newton coeffitients
by Rafa{\l} Kwiatek

NFCONT_1, miz file
The Continuous Functions on Normed Linear Spaces
by Takaya Nishiyama, Keiji Ohkubo and Yasunari Shidama

NFCONT_2, miz file
The Uniform Continuity of Functions on Normed Linear Spaces
by Takaya Nishiyama , Artur Korni{\l}owicz and Yasunari Shidama

NORMFORM, miz file
Algebra of Normal Forms
by Andrzej Trybulec

NORMSP_1, miz file
Real Normed Space
by Jan Popio{\l}ek

NUMBERS, miz file
Subsets of Complex Numbers
by Andrzej Trybulec

NUMERALS, miz file
Numerals - Requirements
by Library Committee

Ordered Rings - Part I
by Micha{\l} Muzalewski and Les{\l}aw W. Szczerba

O_RING_2, miz file
Ordered Rings - Part II
by Micha{\l} Muzalewski and Les{\l}aw W. Szczerba

O_RING_3, miz file
Ordered Rings - Part III
by Micha{\l} Muzalewski and Les{\l}aw W. Szczerba

OPENLATT, miz file
Representation Theorem for Heyting Lattices
by Jolanta Kamie\'nska

OPOSET_1, miz file
Basic Notions and Properties of Orthoposets
by Markus Moschner

OPPCAT_1, miz file
Opposite Categories and Contravariant Functors
by Czes\l aw Byli\'nski

ORDERS_1, miz file
Partially Ordered Sets
by Wojciech A. Trybulec

ORDERS_2, miz file
Kuratowski - Zorn Lemma
by Wojciech A. Trybulec and Grzegorz Bancerek

ORDERS_3, miz file
On the Category of Posets
by Adam Grabowski

ORDERS_4, miz file
On the Isomorphism Between Finite Chains
by Marta Pruszy\'nska and Marek Dudzicz

ORDINAL1, miz file
The Ordinal Numbers. Transfinite Induction and Defining by
Transfinite Induction

ORDINAL2, miz file
Sequences of Ordinal Numbers. Beginnings of Ordinal Arithmetics
by Grzegorz Bancerek

ORDINAL3, miz file
Ordinal Arithmetics
by Grzegorz Bancerek

ORDINAL4, miz file
Increasing and Continuous Ordinal Sequences
by Grzegorz Bancerek

ORTSP_1, miz file
Construction of a bilinear symmetric form in orthogonal vector space
by Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski

OSAFREE, miz file
Free Order Sorted Universal Algebra
by Josef Urban

OSALG_1, miz file
Order Sorted Algebras
by Josef Urban

OSALG_2, miz file
Subalgebras of a Order Sorted Algebra. {L}attice of Subalgebras
by Josef Urban

OSALG_3, miz file
Homomorphisms of Order Sorted Algebras
by Josef Urban

OSALG_4, miz file
Order Sorted Quotient Algebra
by Josef Urban

Fanoian, Pappian and Desarguesian Affine Spaces
by Krzysztof Pra\.zmowski

PARDEPAP, miz file
Elementary Variants of Affine Configurational Theorems
by Krzysztof Pra\.zmowski and Krzysztof Radziszewski

PARSP_1, miz file
Parallelity Spaces
by Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski

PARSP_2, miz file
Fano-Desargues Parallelity Spaces
by Eugeniusz Kusak and Wojciech Leo\'nczuk

PARTFUN1, miz file
Partial Functions
by Czes{\l}aw Byli\'nski

PARTFUN2, miz file
Partial Functions from a Domain to a Domain
by Jaros{\l}aw Kotowicz

PARTFUN3, miz file
On the Real Valued Functions
by Artur Korni{\l}owicz

PARTIT1, miz file
A theory of partitions, { I }
by Shunichi Kobayashi and Kui Jia

PARTIT_2, miz file
Classes of Independent Partitions
by Andrzej Trybulec

PASCH, miz file
Classical and Non--classical Pasch Configurations in Ordered Affine Planes
by Henryk Oryszczyszyn, Krzysztof Pra\.zmowski and

PBOOLE, miz file
Manysorted Sets
by Andrzej Trybulec

PCOMPS_1, miz file
Paracompact and Metrizable Spaces
by Leszek Borys

PCOMPS_2, miz file
On Paracompactness of Metrizable Spaces
by Leszek Borys

PENCIL_1, miz file
On Segre's Product of Partial Line Spaces
by Adam Naumowicz

PENCIL_2, miz file
On Cosets in Segre's Product of Partial Linear Spaces
by Adam Naumowicz

PENCIL_3, miz file
On the Characterization of Collineations of the Segre Product of Strongly
Connected Partial Linear Spaces

PENCIL_4, miz file
Spaces of Pencils, {G}rassmann Spaces, and Generalized {V}eronese
Spaces

PEPIN, miz file
Public-Key Cryptography and Pepin's Test for the Primality of
Fermat Numbers

PETRI, miz file
Basic Petri Net Concepts.
Place/Transition Net Structure, Deadlocks, Traps, Dual Nets

PNPROC_1, miz file
Processes in {P}etri nets
by Grzegorz Bancerek , Mitsuru Aoki , Akio Matsumoto and Yasunari Shidama

POLYALG1, miz file
The Algebra of Polynomials
by Ewa Gr\c{a}dzka

POLYEQ_1, miz file
Solving Roots of Polynomial Equations of Degree 2 and 3 with
Real Coefficients

POLYEQ_2, miz file
Solving Roots of Polynomial Equation of Degree 4 with Real Coefficients
by Xiquan Liang

POLYEQ_3, miz file
Solving Complex Roots of Polynomial Equation of Degree 2 and 3 with
Complex Coefficients

POLYEQ_4, miz file
Solving the Roots of the Special Polynomial Equation with Real
Coefficients

POLYNOM1, miz file
Multivariate polynomials with arbitrary number of variables
by Piotr Rudnicki and Andrzej Trybulec

POLYNOM2, miz file
Evaluation of Multivariate Polynomials
by Christoph Schwarzweller and Andrzej Trybulec

POLYNOM3, miz file
The Ring of Polynomials
by Robert Milewski

POLYNOM4, miz file
Evaluation of Polynomials
by Robert Milewski

POLYNOM5, miz file
Fundamental Theorem of Algebra
by Robert Milewski

POLYNOM6, miz file
On polynomials with coefficients in a ring of polynomials
by Barbara Dzienis

POLYNOM7, miz file
More About Polynomials: Monomials and Constant Polynomials
by Christoph Schwarzweller

POLYRED, miz file
Polynomial Reduction
by Christoph Schwarzweller

POWER, miz file
Real Exponents and Logarithms
by Konrad Raczkowski and Andrzej N\c{e}dzusiak

PRALG_1, miz file
Product of Family of Universal Algebras
by Beata Madras

PRALG_2, miz file
Products of Many Sorted Algebras
by Beata Madras

PRALG_3, miz file
More on Products of Many Sorted Algebras
by Mariusz Giero

PRE_CIRC, miz file
Preliminaries to Circuits, I
by Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec and Pauline N. Kawamo

PRE_FF, miz file
Two Programs for {\bf SCM}. Part I - Preliminaries
by Grzegorz Bancerek and Piotr Rudnicki

PRE_TOPC, miz file
Topological Spaces and Continuous Functions
by Beata Padlewska and Agata Darmochwa\l

PRELAMB, miz file
Preliminaries to the Lambek Calculus
by Wojciech Zielonka

PREPOWER, miz file
Integer and Rational Exponents
by Konrad Raczkowski

PRGCOR_1, miz file
Correctness of Non Overwriting Programs. {P}art {I}
by Yatsuka Nakamura

PRGCOR_2, miz file
Logical Correctness of Vector Calculation Programs
by Takaya Nishiyama , Hirofumi Fukura and Yatsuka Nakamura

PROB_1, miz file
$\sigma$-Fields and Probability
by Andrzej N\c{e}dzusiak

PROB_2, miz file
Probability. Independence of Events and Conditional Probability
by Andrzej N\c{e}dzusiak

PROB_3, miz file
Set Sequences and Monotone Class
by Bo Zhang , Hiroshi Yamazaki and Yatsuka Nakamura

PROB_4, miz file
The Relevance of Measure and Probability and Definition of Completeness
of Probability

PROCAL_1, miz file
Calculus of Propositions
by Jan Popio{\l}ek and Andrzej Trybulec

PROJDES1, miz file
Desargues Theorem In Projective 3-Space
by Eugeniusz Kusak

PROJPL_1, miz file
Projective {P}lanes
by Micha{\l} Muzalewski

PROJRED1, miz file
Incidence Projective Space (a reduction theorem in a plane)
by Eugeniusz Kusak and Wojciech Leo\'nczuk

PROJRED2, miz file
On Projections in Projective Planes. Part II
by Eugeniusz Kusak, Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski

PRVECT_1, miz file
Product of Families of Groups and Vector Spaces
by Anna Lango and Grzegorz Bancerek

PSCOMP_1, miz file
Bounding boxes for compact sets in ${\calE}^2$
by Czes{\l}aw Byli\'nski and Piotr Rudnicki

PUA2MSS1, miz file
Minimal Manysorted Signature for Partial Algebra
by Grzegorz Bancerek

PYTHTRIP, miz file
Pythagorean triples
by Freek Wiedijk

PZFMISC1, miz file
Some Basic Properties of Many Sorted Sets
by Artur Korni{\l}owicz

A First Order Language
by Piotr Rudnicki and Andrzej Trybulec

QC_LANG2, miz file
Connectives and Subformulae of the First Order Language
by Grzegorz Bancerek

QC_LANG3, miz file
Variables in Formulae of the First Order Language
by Czes{\l}aw Byli\'nski and Grzegorz Bancerek

QC_LANG4, miz file
The Subformula Tree of a Formula of the First Order Language
by Oleg Okhotnikov

QMAX_1, miz file
The Fundamental Logic Structure in Quantum Mechanics
by Pawe{\l} Sadowski, Andrzej Trybulec and Konrad Raczkowski

QUANTAL1, miz file
Quantales
by Grzegorz Bancerek

QUIN_1, miz file
Quadratic Inequalities
by Jan Popio\l ek

QUOFIELD, miz file
The Field of Quotients over an Integral Domain
by Christoph Schwarzweller

Definitions of Radix-2k Signed-Digit number and its adder algorithm
by Yoshinori Fujisawa and Yasushi Fuwa

RADIX_2, miz file
High-speed algorithms for RSA cryptograms
by Yasushi Fuwa and Yoshinori Fujisawa

RADIX_3, miz file
Improvement of Radix-$2^k$ Signed-Digit Number for High Speed Circuit
by Masaaki Niimura and Yasushi Fuwa

RADIX_4, miz file
High Speed Adder Algorithm with Radix-$2^k$ SD_Sub Number
by Masaaki Niimura and Yasushi Fuwa

RADIX_5, miz file
Magnitude Relation Properties of Radix-$2^k$ SD Number
by Masaaki Niimura and Yasushi Fuwa

RADIX_6, miz file
High Speed Modulo Calculation Algorithm with Radix-$2^k$ SD Number
by Masaaki Niimura and Yasushi Fuwa

RAT_1, miz file
Basic Properties of Rational Numbers
by Andrzej Kondracki

RCOMP_1, miz file
Topological Properties of Subsets in Real Numbers
by Konrad Raczkowski and Pawe{\l} Sadowski

RCOMP_2, miz file
Half Open Intervals in Real Numbers
by Yatsuka Nakamura

RCOMP_3, miz file
Properties of Connected Subsets of the Real Line
by Artur Korni{\l}owicz

REAL, miz file
Basic Properties of Real Numbers - Requirements
by Library Committee

REAL_1, miz file
Basic Properties of Real Numbers
by Krzysztof Hryniewiecki

REAL_2, miz file
Equalities and Inequalities in Real Numbers. Continuation of REAL_1
by Andrzej Kondracki

REAL_LAT, miz file
The Lattice of Real Numbers. The Lattice of Real Functions
by Marek Chmur

REAL_NS1, miz file
Completeness of the Real {E}uclidean Space
by Noboru Endou and Yasunari Shidama

REALSET1, miz file
Group and Field Definitions
by J\'ozef Bia{\l}as

REALSET2, miz file
Properties of Fields
by J\'ozef Bia{\l}as

REALSET3, miz file
Several Properties of Fields. Field Theory
by J\'ozef Bia{\l}as

REARRAN1, miz file
Introduction to Theory of Rearrangment
by Yuji Sakai and Jaros{\l}aw Kotowicz

RECDEF_1, miz file
Recursive Definitions
by Krzysztof Hryniewiecki

RECDEF_2, miz file
Recursive Definitions. {P}art {II}
by Artur Korni{\l}owicz

RELAT_1, miz file
Relations and Their Basic Properties
by Edmund Woronowicz

RELAT_2, miz file
Properties of Binary Relations
by Edmund Woronowicz and Anna Zalewska

RELOC, miz file
Relocatability
by Yasushi Tanaka

RELSET_1, miz file
Relations Defined on Sets
by Edmund Woronowicz

RELSET_2, miz file
Properties of First and Second Order Cutting of Binary Relations
by Krzysztof Retel

REVROT_1, miz file
Rotating and reversing.(Finite sequences)
by Andrzej Trybulec

REWRITE1, miz file
Reduction Relations
by Grzegorz Bancerek

RFINSEQ, miz file
Functions and Finite Sequences of Real Numbers
by Jaros{\l}aw Kotowicz

RFINSEQ2, miz file
Sorting Operators for Finite Sequences
by Yatsuka Nakamura

RFUNCT_1, miz file
Partial Functions from a Domain to the Set of Real Numbers
by Jaros{\l}aw Kotowicz

RFUNCT_2, miz file
Properties of Real Functions
by Jaros{\l}aw Kotowicz

RFUNCT_3, miz file
Properties of Partial Functions from a Domain to the Set of Real Numbers
by Jaros{\l}aw Kotowicz and Yuji Sakai

RFUNCT_4, miz file
Introduction to Several Concepts of Convexity and Semicontinuity
for Function from REAL to REAL

RINFSUP1, miz file
Inferior Limit and Superior Limit of Sequences of Real Numbers
by Bo Zhang , Hiroshi Yamazaki and Yatsuka Nakamura

RING_1, miz file
Quotient Rings
by Artur Korni{\l}owicz

RINGCAT1, miz file
Category of Rings
by Micha{\l} Muzalewski

RLSUB_1, miz file
Subspaces and Cosets of Subspaces in Real Linear Space
by Wojciech A. Trybulec

RLSUB_2, miz file
Operations on Subspaces in Real Linear Space
by Wojciech A. Trybulec

RLTOPSP1, miz file
Introduction to Real Linear Topological Spaces
by Czes{\l}aw Byli\'nski

RLVECT_1, miz file
Vectors in Real Linear Space
by Wojciech A. Trybulec

RLVECT_2, miz file
Linear Combinations in Real Linear Space
by Wojciech A. Trybulec

RLVECT_3, miz file
Basis of Real Linear Space
by Wojciech A. Trybulec

RLVECT_4, miz file
Subspaces of Real Linear Space Generated by One, Two, or Three Vectors
and Their Cosets

RLVECT_5, miz file
The Steinitz Theorem and the Dimension of a Real Linear Space
by JingChao Chen

RMOD_2, miz file
Submodules and Cosets of Submodules in Right Module over Associative Ring
by Michal Muzalewski and Wojciech Skaba

RMOD_3, miz file
Operations on Submodules in Right Module over Associative Ring
by Michal Muzalewski and Wojciech Skaba

RMOD_4, miz file
Linear Combinations in Right Module over Associative Ring
by Michal Muzalewski and Wojciech Skaba

RMOD_5, miz file
Linear Independence in Right Module over Domain
by Michal Muzalewski and Wojciech Skaba

ROBBINS1, miz file
Robbins Algebras vs. Boolean Algebras
by Adam Grabowski

ROBBINS2, miz file
On the Two Short Axiomatizations of Ortholattices
by Wioletta Truszkowska and Adam Grabowski

ROBBINS3, miz file
Formalization of Ortholattices via Orthoposets
by Adam Grabowski and Markus Moschner

ROLLE, miz file
Average Value Theorems for Real Functions of One Variable
by Jaros{\l}aw Kotowicz, Konrad Raczkowski and Pawe{\l} Sadowski

ROUGHS_1, miz file
Basic Properties of Rough Sets and Rough Membership Function
by Adam Grabowski

RPR_1, miz file
Introduction to Probability
by Jan Popio{\l}ek

RSSPACE, miz file
Real Linear Space of Real Sequences
by Noboru Endou , Yasumasa Suzuki and Yasunari Shidama

RSSPACE2, miz file
Hilbert Space of Real Sequences
by Noboru Endou , Yasumasa Suzuki and Yasunari Shidama

RSSPACE3, miz file
Banach Space of Absolute Summable Real Sequences
by Yasumasa Suzuki, Noboru Endou and Yasunari Shidama

RSSPACE4, miz file
Banach Space of Bounded Real Sequences
by Yasumasa Suzuki

RUSUB_1, miz file
Subspaces and Cosets of Subspace of Real Unitary Space
by Noboru Endou , Takashi Mitsuishi and Yasunari Shidama

RUSUB_2, miz file
Operations on Subspaces in Real Unitary Space
by Noboru Endou , Takashi Mitsuishi and Yasunari Shidama

RUSUB_3, miz file
Linear Combinations in Real Unitary Space
by Noboru Endou , Takashi Mitsuishi and Yasunari Shidama

RUSUB_4, miz file
Dimension of Real Unitary Space
by Noboru Endou , Takashi Mitsuishi and Yasunari Shidama

RUSUB_5, miz file
Topology of Real Unitary Space
by Noboru Endou , Takashi Mitsuishi and Yasunari Shidama

RVSUM_1, miz file
The Sum and Product of Finite Sequences of Real Numbers
by Czes{\l}aw Byli\'nski

Schemes of Existence of some Types of Functions
by Jaros{\l}aw Kotowicz

SCHEMS_1, miz file
Schemes
by Stanis\l aw T. Czuba

SCM_1, miz file
Development of Terminology for {\bf SCM}
by Grzegorz Bancerek and Piotr Rudnicki

SCM_COMP, miz file
A compiler of arithmetic expressions for { \bf SCM }
by Grzegorz Bancerek and Piotr Rudnicki

SCM_HALT, miz file
Initialization Halting Concepts and Their Basic Properties of SCM+FSA
by JingChao Chen and Yatsuka Nakamura

SCMBSORT, miz file
Bubble Sort on SCM+FSA
by JingChao Chen and Yatsuka Nakamura

SCMFSA10, miz file
On the Instructions of { \bf SCM+FSA }
by Artur Korni{\l}owicz

SCMFSA6A, miz file
On the compositions of macro instructions
by Andrzej Trybulec , Yatsuka Nakamura and Noriko Asamoto

SCMFSA6B, miz file
On the compositions of macro instructions, Part II
by Noriko Asamoto , Yatsuka Nakamura , Piotr Rudnicki and Andrzej Trybulec

SCMFSA6C, miz file
On the compositions of macro instructions, Part III
by Noriko Asamoto , Yatsuka Nakamura , Piotr Rudnicki and Andrzej Trybulec

SCMFSA7B, miz file
Constant assignment macro instructions of SCM+FSA, Part II
by Noriko Asamoto

SCMFSA8A, miz file
Conditional branch macro instructions of SCM+FSA, Part I (preliminary)
by Noriko Asamoto

SCMFSA8B, miz file
Conditional branch macro instructions of SCM+FSA, Part II
by Noriko Asamoto

SCMFSA8C, miz file
The {\bf loop} and {\bf Times} Macroinstruction for {\SCMFSA}
by Noriko Asamoto

SCMFSA9A, miz file
The { \bf while } macro instructions of SCM+FSA, Part { II }
by Piotr Rudnicki

SCMFSA_1, miz file
An Extension of { \bf SCM }
by Andrzej Trybulec , Yatsuka Nakamura and Piotr Rudnicki

SCMFSA_2, miz file
The { \bf SCM_FSA } computer
by Andrzej Trybulec , Yatsuka Nakamura and Piotr Rudnicki

SCMFSA_3, miz file
Computation in { \bf SCM_FSA }
by Andrzej Trybulec and Yatsuka Nakamura

SCMFSA_4, miz file
Modifying addresses of instructions of { \bf SCM_FSA }
by Andrzej Trybulec and Yatsuka Nakamura

SCMFSA_5, miz file
Relocability for { \bf SCM_FSA }
by Andrzej Trybulec and Yatsuka Nakamura

SCMFSA_7, miz file
Some Multi-instructions defined by sequence of instructions of SCM+FSA
by Noriko Asamoto

SCMFSA_9, miz file
While Macro Instructions of SCM+FSA
by Jing-Chao Chen

SCMISORT, miz file
Insert Sort on SCM+FSA
by JingChao Chen

SCMP_GCD, miz file
Recursive Euclide Algorithm
by JingChao Chen

SCMPDS_1, miz file
A Small Computer Model with Push-Down Stack
by JingChao Chen

SCMPDS_2, miz file
The SCMPDS Computer and the Basic Semantics of Its Instructions
by JingChao Chen

SCMPDS_3, miz file
Computation and Program Shift in the SCMPDS Computer
by JingChao Chen

SCMPDS_4, miz file
The Construction and shiftability of Program Blocks for SCMPDS
by JingChao Chen

SCMPDS_5, miz file
Computation of Two Consecutive Program Blocks for SCMPDS
by JingChao Chen

SCMPDS_6, miz file
The Construction and Computation of Conditional Statements for SCMPDS
by JingChao Chen

SCMPDS_7, miz file
The Construction and Computation of For-loop Programs for SCMPDS
by JingChao Chen and Piotr Rudnicki

SCMPDS_8, miz file
The Construction and Computation of While-loop Programs for SCMPDS
by JingChao Chen

SCMPDS_9, miz file
SCMPDS Is Not Standard
by Artur Korni{\l}owicz and Yasunari Shidama

SCMRING1, miz file
The Construction of { \bf SCM } over Ring
by Artur Korni{\l}owicz

SCMRING2, miz file
The Basic Properties of { \bf SCM } over Ring
by Artur Korni{\l}owicz

SCMRING3, miz file
The Properties of Instructions of { \bf SCM } over Ring
by Artur Korni{\l}owicz

SCMRING4, miz file
Relocability for { \bf SCM } over Ring
by Artur Korni{\l}owicz and Yasunari Shidama

SCPINVAR, miz file
Justifying the Correctness of Fibonacci Sequence and Euclide
Algorithm by Loop Invariant

SCPISORT, miz file
Insert Sort on SCMPDS
by JingChao Chen

SCPQSORT, miz file
Quick Sort on SCMPDS
by JingChao Chen

SEMI_AF1, miz file
Semi-Affine Space
by Eugeniusz Kusak and Krzysztof Radziszewski

SEQ_1, miz file
Real Sequences and Basic Operations on Them
by Jaros{\l}aw Kotowicz

SEQ_2, miz file
Convergent Sequences and the Limit of Sequences
by Jaros{\l}aw Kotowicz

SEQ_4, miz file
Convergent Real Sequences. Upper and Lower Bound of Sets of Real Numbers
by Jaros{\l}aw Kotowicz

SEQFUNC, miz file
Functional Sequence from a Domain to a Domain
by Beata Perkowska

SEQM_3, miz file
Monotone Real Sequences. Subsequences
by Jaros{\l}aw Kotowicz

SERIES_1, miz file
Series
by Konrad Raczkowski and Andrzej N\c{e}dzusiak

SERIES_2, miz file
Partial Sum of Some Series
by Ming Liang and Yuzhong Ding

SERIES_3, miz file
On the Partial Product of Series and Related Basic Inequalities
by Fuguo Ge and Xiquan Liang

SERIES_4, miz file
Partial Sum and Partial Product of Some Series
by Jianbing Cao , Fahui Zhai and Xiquan Liang

SERIES_5, miz file
On the Partial Product and Partial Sum of Series and Related Basic
Inequalities

SETFAM_1, miz file
Families of Sets
by Beata Padlewska

SETLIM_1, miz file
Limit of Sequence of Subsets
by Bo Zhang , Hiroshi Yamazaki and Yatsuka Nakamura

SETLIM_2, miz file
Some Equations Related to the Limit of Sequence of Subsets
by Bo Zhang , Hiroshi Yamazaki and Yatsuka Nakamura

SETWISEO, miz file
Semilattice Operations on Finite Subsets
by Andrzej Trybulec

SETWOP_2, miz file
Semigroup operations on finite subsets
by Czes{\l}aw Byli\'nski

SF_MASTR, miz file
Memory handling for SCM+FSA
by Piotr Rudnicki and Andrzej Trybulec

SFMASTR1, miz file
On the Composition of non-parahalting Macro Instructions
by Piotr Rudnicki

SFMASTR2, miz file
Another { \bf times } Macro Instruction
by Piotr Rudnicki

SFMASTR3, miz file
The { \bf for } (going up) Macro Instruction
by Piotr Rudnicki

SGRAPH1, miz file
The Formalisation of Simple Graphs
by Yozo Toda

SHEFFER1, miz file
Axiomatization of {B}oolean Algebras Based on Sheffer Stroke
by Violetta Kozarkiewicz and Adam Grabowski

SHEFFER2, miz file
Short {S}heffer Stroke-Based Single Axiom for {B}oolean Algebras
by Aneta {\L}ukaszuk and Adam Grabowski

SIN_COS, miz file
Trigonometric Functions and Existence of Circle Ratio
by Yuguang Yang and Yasunari Shidama

SIN_COS2, miz file
Properties of Trigonometric Function
by Takashi Mitsuishi and Yuguang Yang

SIN_COS3, miz file
Trigonometric Functions on Complex Space
by Takashi Mitsuishi , Noboru Endou and Keiji Ohkubo

SIN_COS4, miz file
Formulas And Identities of Trigonometric Functions
by Pacharapokin Chanapat, Kanchun and Hiroshi Yamazaki

SIN_COS5, miz file
Formulas And Identities of Trigonometric Functions
by Yuzhong Ding and Xiquan Liang

SIN_COS6, miz file
Inverse Trigonometric Functions Arcsin and Arccos
by Artur Korni{\l}owicz and Yasunari Shidama

SIN_COS7, miz file
Formulas And Identities of Inverse Hyperbolic Functions
by Fuguo Ge , Xiquan Liang and Yuzhong Ding

SIN_COS8, miz file
Formulas and Identities of Hyperbolic Functions
by Pacharapokin Chanapat and Hiroshi Yamazaki

SPPOL_1, miz file
Extremal Properties of Vertices on Special Polygons I
by Yatsuka Nakamura and Czes\law Byli\'nski

SPPOL_2, miz file
Special Polygons
by Czes\law Byli\'nski and Yatsuka Nakamura

SPRECT_1, miz file
On Rectangular Finite Sequences of the Points of the Plane
by Andrzej Trybulec and Yatsuka Nakamura

SPRECT_2, miz file
On the Order on a Special Polygon
by Andrzej Trybulec and Yatsuka Nakamura

SPRECT_3, miz file
Some properties of special polygonal curves
by Andrzej Trybulec and Yatsuka Nakamura

SPRECT_4, miz file
On the components of the complement of a special polygonal curve
by Andrzej Trybulec and Yatsuka Nakamura

SPRECT_5, miz file
Again on the Order on a Special Polygon
by Andrzej Trybulec and Yatsuka Nakamura

SQUARE_1, miz file
Some Properties of Real Numbers.
Operations: min, max, square, and square root

STIRL2_1, miz file
Stirling Numbers of the Second Kind
by Karol P\c{a}k

STRUCT_0, miz file
Preliminaries to Structures
by Library Committee

SUB_METR, miz file
Submetric Spaces - Part I
by Adam Lecko and Mariusz Startek

SUBLEMMA, miz file
Coincidence Lemma and Substitution Lemma
by Patrick Braselmann and Peter Koepke

SUBSET, miz file
Basic Properties of Subsets - Requirements
by Library Committee

SUBSET_1, miz file
Properties of Subsets
by Zinaida Trybulec

SUBSTLAT, miz file
Lattice of Substitutions
by Adam Grabowski

SUBSTUT1, miz file
Substitution in First-Order Formulas: Elementary Properties
by Patrick Braselmann and Peter Koepke

SUBSTUT2, miz file
Substitution in First-Order Formulas -- Part II. {T}he Construction of
First-Order Formulas

SUPINF_1, miz file
Infimum and Supremum of the Set of Real Numbers. Measure Theory
by J\'ozef Bia{\l}as

SUPINF_2, miz file
Series of Positive Real Numbers. Measure Theory
by J\'ozef Bia{\l}as

SYMSP_1, miz file
Construction of a bilinear antisymmetric form in symplectic vector space
by Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski

SYSREL, miz file
Some Properties of Binary Relations
by Waldemar Korczy\'nski

$T_0$ Topological Spaces
by Mariusz \.Zynel and Adam Guzowski

T_1TOPSP, miz file
On $T_{1}$ Reflex of Topological Space
by Adam Naumowicz and Mariusz {\L}api\'nski

TARSKI, miz file
Tarski Grothendieck Set Theory
by Andrzej Trybulec

TAXONOM1, miz file
Lower Tolerance. {P}reliminaries to {W}roclaw Taxonomy
by Mariusz Giero and Roman Matuszewski

TAXONOM2, miz file
Hierarchies and Classifications of Sets
by Mariusz Giero

TAYLOR_1, miz file
The {T}aylor Expansions
by Yasunari Shidama

TAYLOR_2, miz file
The {M}aclaurin Expansions
by Akira Nishino and Yasunari Shidama

TBSP_1, miz file
Totally Bounded Metric Spaces
by Alicia de la Cruz

TDGROUP, miz file
A Construction of an Abstract Space of Congruence of Vectors
by Grzegorz Lewandowski and Krzysztof Pra\.zmowski

TDLAT_1, miz file
The Lattice of Domains_of of a Topological Space
by Toshihiko Watanabe

TDLAT_2, miz file
Completeness of the Lattices of Domains of a Topological Space
by Zbigniew Karno and Toshihiko Watanabe

TDLAT_3, miz file
The Lattice of Domains of an Extremally Disconnected Space
by Zbigniew Karno

TERMORD, miz file
Term Orders
by Christoph Schwarzweller

TEX_1, miz file
On Discrete and Almost Discrete Topological Spaces
by Zbigniew Karno

TEX_2, miz file
Maximal Discrete Subspaces of Almost Discrete Topological Spaces
by Zbigniew Karno

TEX_3, miz file
On Nowhere and Everywhere Dense Subspaces of Topological Spaces
by Zbigniew Karno

TEX_4, miz file
Maximal Anti-Discrete Subspaces of Topological Spaces
by Zbigniew Karno

TIETZE, miz file
Tietze {E}xtension {T}heorem
by Artur Korni{\l}owicz , Grzegorz Bancerek and Adam Naumowicz

TMAP_1, miz file
Continuity of Mappings over the Union of Subspaces
by Zbigniew Karno

TOLER_1, miz file
Relations of Tolerance
by Krzysztof Hryniewiecki

TOPALG_1, miz file
The Fundamental Group
by Artur Korni{\l}owicz , Yasunari Shidama and Adam Grabowski

TOPALG_2, miz file
The Fundamental Group of Convex Subspaces of TOP-REAL n
by Artur Korni{\l}owicz

TOPALG_3, miz file
On the Isomorphism of Fundamental Groups
by Artur Korni{\l}owicz

TOPALG_4, miz file
On the Fundamental Groups of Products of Topological Spaces
by Artur Korni{\l}owicz

TOPALG_5, miz file
The Fundamental Group of the Circle
by Artur Korni{\l}owicz

TOPGEN_1, miz file
On the Boundary and Derivative of a Set
by Adam Grabowski

TOPGEN_2, miz file
On the characteristic and weight of a topological space
by Grzegorz Bancerek

TOPGEN_3, miz file
On constructing topological spaces and Sorgenfrey line
by Grzegorz Bancerek

TOPGEN_4, miz file
On the {B}orel Families of Subsets of Topological Spaces
by Adam Grabowski

TOPGEN_5, miz file
Niemytzki Plane -- an Example of {T}ychonoff Space Which Is Not $T_4$
by Grzegorz Bancerek

TOPGRP_1, miz file
The Definition and Basic Properties of Topological Groups
by Artur Korni{\l}owicz

TOPMETR, miz file
Metric Spaces as Topological Spaces - Fundamental Concepts
by Agata Darmochwa{\l} and Yatsuka Nakamura

TOPMETR2, miz file
Some Facts about Union of Two Functions and Continuity of Union of Functions

TOPMETR3, miz file
Sequences of Metric Spaces and an Abstract Intermediate Value Theorem
by Yatsuka Nakamura and Andrzej Trybulec

TOPREAL1, miz file
The Topological Space ${\calE}^2_{\rm T}$.
Arcs, Line Segments and Special Polygonal Arcs

TOPREAL2, miz file
The Topological Space ${\calE}^2_{\rm T}$. Simple Closed Curves
by Agata Darmochwa{\l} and Yatsuka Nakamura

TOPREAL3, miz file
Basic Properties of Connecting Points with Line Segments
in ${\calE}^2_{\rm T}$

TOPREAL4, miz file
Connectedness Conditions Using Polygonal Arcs
by Yatsuka Nakamura and Jaros{\l}aw Kotowicz

TOPREAL5, miz file
Intermediate Value Theorem and Thickness of Simple Closed Curves
by Yatsuka Nakamura and Andrzej Trybulec

TOPREAL6, miz file
Compactness of the Bounded Closed Subsets of TOP-REAL 2
by Artur Korni{\l}owicz

TOPREAL7, miz file
Homeomorphism between [:TOP-REAL i,TOP-REAL j:] and TOP-REAL (i+j)
by Artur Korni{\l}owicz

TOPREAL8, miz file
More on the Finite Sequences on the Plane
by Andrzej Trybulec

TOPREAL9, miz file
Intersections of Intervals and Balls in TOP-REAL n
by Artur Korni{\l}owicz and Yasunari Shidama

TOPREALA, miz file
Some Properties of Rectangles on the Plane
by Artur Korni{\l}owicz and Yasunari Shidama

TOPREALB, miz file
Some Properties of Circles on the Plane
by Artur Korni{\l}owicz and Yasunari Shidama

TOPRNS_1, miz file
Sequences in $R^n$
by Agnieszka Sakowicz , Jaros{\l}aw Gryko and Adam Grabowski

TOPS_1, miz file
Subsets of Topological Spaces
by Miros{\l}aw Wysocki and Agata Darmochwa\l

TOPS_2, miz file
Families of Subsets, Subspaces and Mappings in Topological Spaces
by Agata Darmochwa{\l}

TOPS_3, miz file
Remarks on Special Subsets of Topological Spaces
by Zbigniew Karno

TRANSGEO, miz file
Transformations in Affine Spaces
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

TRANSLAC, miz file
Translations in Affine Planes
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski

TREAL_1, miz file
The Brouwer Fixed Point Theorem for Intervals
by Toshihiko Watanabe

TREES_1, miz file
Introduction to Trees
by Grzegorz Bancerek

TREES_2, miz file
K\"onig's Lemma
by Grzegorz Bancerek

TREES_3, miz file
Sets and Functions of Trees and Joining Operations of Trees
by Grzegorz Bancerek

TREES_4, miz file
Joining of Decorated Trees
by Grzegorz Bancerek

TREES_9, miz file
Subtrees
by Grzegorz Bancerek

TREES_A, miz file
Replacement of Subtrees in a Tree
by Oleg Okhotnikov

TRIANG_1, miz file
On the concept of the triangulation
by Beata Madras

TSEP_1, miz file
Separated and Weakly Separated Subspaces of Topological Spaces
by Zbigniew Karno

TSEP_2, miz file
On a Duality Between Weakly Separated Subspaces of Topological Spaces
by Zbigniew Karno

TSP_1, miz file
On Kolmogorov Topological Spaces
by Zbigniew Karno

TSP_2, miz file
Maximal Kolmogorov Subspaces of a Topological Space as Stone
Retracts of the Ambient Space

TURING_1, miz file
Introduction to Turing Machines
by Jingchao Chen and Yatsuka Nakamura

TWOSCOMP, miz file
2's Complement Circuit. Part I. Boolean Operators and 2's
Complement Circuit Properties

Basic Notation of Universal Algebra
by Jaros{\l}aw Kotowicz, Beata Madras and Ma{\l}gorzata Korolkiewicz

UNIALG_2, miz file
Subalgebras of the Universal Algebra. Lattices of Subalgebras
by Ewa Burakowska

UNIALG_3, miz file
On the Lattice of Subalgebras of a Universal Algebra
by Miros{\l}aw Jan Paszek

UNIFORM1, miz file
Lebesgue's Covering Lemma, Uniform Continuity and Segmentation of Arcs
by Yatsuka Nakamura and Andrzej Trybulec

UNIROOTS, miz file
Primitive Roots of Unity and Cyclotomic Polynomials
by Broderic Arneson and Piotr Rudnicki

UPROOTS, miz file
Little {B}ezout Theorem (Factor Theorem)
by Piotr Rudnicki

URYSOHN1, miz file
Dyadic Numbers and $T_4$ Topological Spaces
by J\'ozef Bia\las and Yatsuka Nakamura

URYSOHN2, miz file
Some Properties of Dyadic Numbers and Intervals
by J\'ozef Bia{\l}as and Yatsuka Nakamura

URYSOHN3, miz file
Urysohn Lemma
by J\'ozef Bia{\l}as and Yatsuka Nakamura

Interpretation and Satisfiability in the First Order Logic
by Edmund Woronowicz

VECTMETR, miz file
Real Linear-Metric Space and Isometric Functions
by Robert Milewski

VECTSP10, miz file
Quotient Vector Spaces and Functionals
by Jaros{\l}aw Kotowicz

VECTSP_1, miz file
Abelian Groups, Fields and Vector Spaces
by Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski

VECTSP_2, miz file
Construction of Rings and Left-, Right-, and Bi-Modules over a Ring
by Micha{\l} Muzalewski

VECTSP_3, miz file
Finite Sums of Vectors in Vector Space
by Wojciech A. Trybulec

VECTSP_4, miz file
Subspaces and Cosets of Subspaces in Vector Space
by Wojciech A. Trybulec

VECTSP_5, miz file
Operations on Subspaces in Vector Space
by Wojciech A. Trybulec

VECTSP_6, miz file
Linear Combinations in Vector Space
by Wojciech A. Trybulec

VECTSP_7, miz file
Basis of Vector Space
by Wojciech A. Trybulec

VECTSP_8, miz file
On the Lattice of Subspaces of Vector Space
by Andrzej Iwaniuk

VECTSP_9, miz file
Steinitz Theorem and Dimension of a Vector Space
by Mariusz \.Zynel

VFUNCT_1, miz file
Algebra of Vector Functions
by Hiroshi Yamazaki and Yasunari Shidama

VFUNCT_2, miz file
Algebra of Complex Vector Valued Functions
by Noboru Endou

Closure Operators and Subalgebras
by Grzegorz Bancerek

WAYBEL11, miz file
Scott Topology
by Andrzej Trybulec

WAYBEL12, miz file
On the Baire Category Theorem
by Artur Korni{\l}owicz

WAYBEL13, miz file
Algebraic and Arithmetic Lattices
by Robert Milewski

WAYBEL14, miz file
The Scott Topology, Part II
by Czes{\l}aw Byli\'nski and Piotr Rudnicki

WAYBEL15, miz file
More on the Algebraic and Arithmetic Lattices
by Robert Milewski

WAYBEL16, miz file
Completely-Irreducible Elements
by Robert Milewski

WAYBEL17, miz file
Scott-Continuous Functions
by Adam Grabowski

WAYBEL18, miz file
Injective Spaces
by Jaros{\l}aw Gryko

WAYBEL19, miz file
The Lawson Topology
by Grzegorz Bancerek

WAYBEL20, miz file
Kernel Projections and Quotient Lattices
by Piotr Rudnicki

WAYBEL21, miz file
Lawson Topology in Continuous Lattices
by Grzegorz Bancerek

WAYBEL22, miz file
Representation theorem for free continuous lattices
by Piotr Rudnicki

WAYBEL23, miz file
Bases of Continuous Lattices
by Robert Milewski

WAYBEL24, miz file
Scott-Continuous Functions, Part II
by Adam Grabowski

WAYBEL25, miz file
Injective Spaces, Part { II }
by Artur Korni{\l}owicz and Jaros{\l}aw Gryko

WAYBEL26, miz file
Continuous Lattices between T$_0$ Spaces
by Grzegorz Bancerek

WAYBEL27, miz file
Function Spaces in the Category of Directed Suprema Preserving Maps
by Grzegorz Bancerek and Adam Naumowicz

WAYBEL28, miz file
Lim-inf Convergence
by Bart{\l}omiej Skorulski

WAYBEL29, miz file
The Characterization of Continuity of Topologies
by Grzegorz Bancerek and Adam Naumowicz

WAYBEL30, miz file
Meet Continuous Lattices Revisited
by Artur Korni{\l}owicz

WAYBEL31, miz file
Weights of Continuous Lattices
by Robert Milewski

WAYBEL32, miz file
On the Order-consistent Topology of Complete and Uncomplete
Lattices

WAYBEL33, miz file
Compactness of Lim-inf Topology
by Grzegorz Bancerek and Noboru Endou

WAYBEL34, miz file
Duality Based on Galois Connection. Part I
by Grzegorz Bancerek

WAYBEL35, miz file
Morphisms Into Chains, Part {I}
by Artur Korni{\l}owicz

WAYBEL_0, miz file
Directed Sets, Nets, Ideals, Filters, and Maps
by Grzegorz Bancerek

WAYBEL_1, miz file
Galois Connections
by Czes\law Byli\'nski

WAYBEL_2, miz file
Meet-continuous Lattices
by Artur Korni{\l}owicz

WAYBEL_3, miz file
The "Way-Below" Relation
by Grzegorz Bancerek

WAYBEL_4, miz file
Auxiliary and Approximating Relations
by Adam Grabowski

WAYBEL_5, miz file
The Equational Characterization of Continuous Lattices
by Mariusz \.Zynel

WAYBEL_6, miz file
Irreducible and Prime Elements
by Beata Madras

WAYBEL_7, miz file
Prime Ideals and Filters
by Grzegorz Bancerek

WAYBEL_8, miz file
Algebraic Lattices
by Robert Milewski

WAYBEL_9, miz file
On The Topological Properties of Meet-Continuous Lattices
by Artur Korni{\l}owicz

WEDDWITT, miz file
Witt's Proof of the {W}edderburn Theorem
by Broderic Arneson , Matthias Baaz and Piotr Rudnicki

WEIERSTR, miz file
The Theorem of Weierstrass
by J\'ozef Bia\las and Yatsuka Nakamura

WELLFND1, miz file
On same equivalents of well-foundedness
by Piotr Rudnicki and Andrzej Trybulec

WELLORD1, miz file
The Well Ordering Relations
by Grzegorz Bancerek

WELLORD2, miz file
Zermelo Theorem and Axiom of Choice. The correspondence of
well ordering relations and ordinal numbers

WELLSET1, miz file
Zermelo's Theorem
by Bogdan Nowak and S{\l}awomir Bia{\l}ecki

WSIERP_1, miz file
The Chinese Remainder Theorem
by Andrzej Kondracki

Boolean Properties of Sets - Definitions
by Library Committee

XBOOLE_1, miz file
Boolean Properties of Sets - Theorems
by Library Committee

XCMPLX_0, miz file
Complex Numbers - Basic Definitions
by Library Committee

XCMPLX_1, miz file
Complex Numbers - Basic Theorems
by Library Committee

XREAL_0, miz file
Introduction to Arithmetic of Real Numbers
by Library Committee

XREAL_1, miz file
Real Numbers - Basic Theorems
by Library Committee

XXREAL_0, miz file
Introduction to Arithmetic of Extended Real Numbers
by Library Committee

The Properties of Product of Relational Structures
by Artur Korni{\l}owicz

YELLOW11, miz file
On the Characterization of Modular and Distributive Lattices
by Adam Naumowicz

YELLOW12, miz file
On the Characterization of {H}ausdorff Spaces
by Artur Korni{\l}owicz

YELLOW13, miz file
Introduction to Meet-Continuous Topological Lattices
by Artur Korni{\l}owicz

YELLOW14, miz file
Some Properties of Isomorphism between Relational Structures. On
the Product of Topological Spaces

YELLOW15, miz file
Components and Basis of Topological Spaces
by Robert Milewski

YELLOW16, miz file
Retracts and Inheritance
by Grzegorz Bancerek

YELLOW17, miz file
The Tichonov Theorem
by Bart{\l}omiej Skorulski

YELLOW18, miz file
Concrete Categories
by Grzegorz Bancerek

YELLOW19, miz file
On the characterizations of compactness
by Grzegorz Bancerek , Noboru Endou and Yuji Sakai

YELLOW20, miz file
Miscellaneous Facts about Functors
by Grzegorz Bancerek

YELLOW21, miz file
Categorial Background for Duality Theory
by Grzegorz Bancerek

YELLOW_0, miz file
Bounds in Posets and Relational Substructures
by Grzegorz Bancerek

YELLOW_1, miz file
Boolean Posets, Posets under Inclusion and Products of Relational
Structures

YELLOW_2, miz file
Properties of Relational Structures, Posets, Lattices and Maps
by Mariusz \.Zynel and Czes{\l}aw Byli\'nski

YELLOW_3, miz file
Cartesian Products of Relations and Relational Structures
by Artur Korni{\l}owicz

YELLOW_4, miz file
Definitions and Properties of the Join and Meet of Subsets
by Artur Korni{\l}owicz

YELLOW_5, miz file
Miscellaneous Facts about Relation Structure
by Agnieszka Julia Marasik

YELLOW_6, miz file
Moore-Smith Convergence
by Andrzej Trybulec

YELLOW_7, miz file
Duality in Relation Structures
by Grzegorz Bancerek

YELLOW_8, miz file
Baire Spaces, Sober Spaces
by Andrzej Trybulec

YELLOW_9, miz file
Bases and Refinements of Topologies
by Grzegorz Bancerek

YONEDA_1, miz file
Yoneda Embedding
by Miros{\l}aw Wojciechowski

The Contraction Lemma
by Grzegorz Bancerek

ZF_FUND1, miz file
Mostowski's Fundamental Operations - Part I
by Andrzej Kondracki

ZF_FUND2, miz file
Mostowski's Fundamental Operations - Part II
by Grzegorz Bancerek and Andrzej Kondracki

ZF_LANG, miz file
A Model of ZF Set Theory Language
by Grzegorz Bancerek

ZF_LANG1, miz file
Replacing of Variables in Formulas of ZF Theory
by Grzegorz Bancerek

ZF_MODEL, miz file
Models and Satisfiability. Defining by Structural Induction and
Free Variables in ZF-formulae

ZF_REFLE, miz file
The Reflection Theorem
by Grzegorz Bancerek

ZFMISC_1, miz file
Some Basic Properties of Sets
by Czes{\l}aw Byli\'nski

ZFMODEL1, miz file
Properties of ZF Models
by Grzegorz Bancerek

ZFMODEL2, miz file
Definable Functions
by Grzegorz Bancerek

ZFREFLE1, miz file
Consequences of the Reflection Theorem
by Grzegorz Bancerek