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 one-to-one 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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