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 two-divisible-groups is singled out, and in the latter, a subclass of uniquely-two-divisible-groups. 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.III-24.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

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[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.
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[10] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received May 23, 1990


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