Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991
Association of Mizar Users
Atlas of Midpoint Algebra

Michal Muzalewski

Warsaw University, Bialystok
Summary.

This article is a continuation of [5].
We have established a onetoone correspondence between midpoint
algebras and groups with the operator 1/2. In general we shall say
that a given midpoint algebra $M$ and a group $V$ are $w$assotiated iff $w$ is
an atlas from $M$ to $V$.
At the beginning of the paper a few facts which rather belong to
[4], [0] are proved.
MML Identifier:
MIDSP_2
The terminology and notation used in this paper have been
introduced in the following articles
[3]
[7]
[2]
[1]
[6]
[4]
[5]
Contents (PDF format)
Bibliography
 [1]
Czeslaw Bylinski.
Binary operations.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions from a set to a set.
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]
Michal Muzalewski.
Midpoint algebras.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
Received June 21, 1991
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