Volume 15, 2003

University of Bialystok

Copyright (c) 2003 Association of Mizar Users

**Freek Wiedijk**- University of Nijmegen

- Translation of pages 101, the second half of 102, and 103 of [16].

This work has been partially supported by CALCULEMUS grant HPRN-CT-2000-00102 and TYPES grant IST-1999-29001.

- Preliminaries
- Gratings, Cells, Chains, Cycles
- Groups and Homomorphisms

- [1]
Grzegorz Bancerek.
Cardinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Grzegorz Bancerek.
The ordinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Grzegorz Bancerek.
K\"onig's theorem.
*Journal of Formalized Mathematics*, 2, 1990. - [5]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Jozef Bialas.
Group and field definitions.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Czeslaw Bylinski.
Binary operations.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [11]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a non-empty sets.
*Journal of Formalized Mathematics*, 2, 1990. - [12]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Agata Darmochwal.
The Euclidean space.
*Journal of Formalized Mathematics*, 3, 1991. - [14]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [15]
Michal Muzalewski.
Opposite rings, modules and their morphisms.
*Journal of Formalized Mathematics*, 4, 1992. - [16] M. H. A. Newman. \em Elements of the Topology of Plane Sets of Points. Cambridge University Press, 1951.
- [17]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
*Journal of Formalized Mathematics*, 1, 1989. - [18]
Piotr Rudnicki and Andrzej Trybulec.
Abian's fixed point theorem.
*Journal of Formalized Mathematics*, 9, 1997. - [19]
Andrzej Trybulec.
Domains and their Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [20]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [21]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [22]
Wojciech A. Trybulec.
Vectors in real linear space.
*Journal of Formalized Mathematics*, 1, 1989. - [23]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [24]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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