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.
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.
Metricaffine configurations in metric affine planes  part I.
Journal of Formalized Mathematics,
2, 1990.
 [6]
Jolanta Swierzynska and Bogdan Swierzynski.
Metricaffine 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
[
Download a postscript version,
MML identifier index,
Mizar home page]