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

Fundamental Types of Metric Affine Spaces


Henryk Oryszczyszyn
Warsaw University, Bialystok
Krzysztof Prazmowski
Warsaw University, Bialystok

Summary.

We distinguish in the class of metric affine spaces some fundamental types of them. First we can assume the underlying affine space to satisfy classical affine configurational axiom; thus we come to Pappian, Desarguesian, Moufangian, and translation spaces. Next we distinguish the spaces satisfying theorem on three perpendiculars and the homogeneous spaces; these properties directly refer to some axioms involving orthogonality. Some known relationships between the introduced classes of structures are established. We also show that the commonly investigated models of metric affine geometry constructed in a real linear space with the help of a symmetric bilinear form belong to all the classes introduced in the paper.

MML Identifier: EUCLMETR

The terminology and notation used in this paper have been introduced in the following articles [8] [1] [7] [3] [4] [2] [6] [5]

Contents (PDF format)

Bibliography

[1] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Henryk Oryszczyszyn and Krzysztof Prazmowski. Analytical metric affine spaces and planes. Journal of Formalized Mathematics, 2, 1990.
[3] Henryk Oryszczyszyn and Krzysztof Prazmowski. Analytical ordered affine spaces. Journal of Formalized Mathematics, 2, 1990.
[4] Henryk Oryszczyszyn and Krzysztof Prazmowski. Ordered affine spaces defined in terms of directed parallelity --- part I. Journal of Formalized Mathematics, 2, 1990.
[5] Jolanta Swierzynska and Bogdan Swierzynski. Metric-affine configurations in metric affine planes --- part I. Journal of Formalized Mathematics, 2, 1990.
[6] Jolanta Swierzynska and Bogdan Swierzynski. Metric-affine configurations in metric affine planes --- part II. Journal of Formalized Mathematics, 2, 1990.
[7] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[8] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

Received April 17, 1991


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