Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Directed Geometrical Bundles and Their Analytical Representation

Grzegorz Lewandowski

Siedlce Agricultural, and Pedagogical University

Krzysztof Prazmowski

Warsaw University, Bialystok

Bozena Lewandowska

Siedlce Agricultural, and Pedagogical University
Summary.

We introduce the notion of weak directed geometrical bundle.
We prove representation theorems for directed and weak directed geometrical
bundles which establishes a onetoone correspondence between such structures
and appropriate 2divisible abelian groups. To this aim we construct over
arbitrary weak directed geometrical bundle a group defined entirely in terms
of geometrical notions  the group of (abstract) ``free vectors".
Supported by RPBP.III24.C3.
MML Identifier:
AFVECT0
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[5]
[11]
[1]
[8]
[7]
[3]
[4]
[2]
[12]
[6]
[10]
Contents (PDF format)
Bibliography
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Group and field definitions.
Journal of Formalized Mathematics,
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Binary operations.
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Functions and their basic properties.
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Some basic properties of sets.
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Abelian groups, fields and vector spaces.
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Relations and their basic properties.
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1, 1989.
Received September 24, 1990
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