Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
A Construction of an Abstract Space of Congruence of Vectors

Grzegorz Lewandowski

Agriculture and Education School, Siedlce

Krzysztof Prazmowski

Warsaw University, Bialystok
Summary.

In the class of abelian groups a
subclass of twodivisiblegroups is singled out, and in the latter,
a subclass of uniquelytwodivisiblegroups. With every such a group
a special geometrical structure, more precisely the
structure of ``congruence of vectors'' is correlated. The notion of
``affine vector space'' (denoted by AffVect) is introduced. This term is defined by
means of suitable axiom system. It is proved that every structure of
the congruence of vectors determined by a non trivial uniquely two
divisible group is a affine vector space.
Supported by RPBP.III24.C3.
MML Identifier:
TDGROUP
The terminology and notation used in this paper have been
introduced in the following articles
[6]
[3]
[9]
[7]
[5]
[2]
[10]
[8]
[4]
[1]
Contents (PDF format)
Bibliography
 [1]
Jozef Bialas.
Group and field definitions.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Analytical ordered affine spaces.
Journal of Formalized Mathematics,
2, 1990.
 [6]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [7]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [8]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
Received May 23, 1990
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