Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
A Construction of Analytical Projective Space

Wojciech Leonczuk

Warsaw University, Bialystok

Supported by RPBP.III24.C6.

Krzysztof Prazmowski

Warsaw University, Bialystok

Supported by RPBP.III24.C2.
Summary.

The collinearity structure denoted by Projec\ti\ve\Spa\ce(V) is correlated
with a given vector space $V$ (over the field of Reals). It is a
formalization of the standard construction of a projective space, where
points are interpreted as equivalence classes of the relation of
proportionality considered in the set of all nonzero vectors. Then the
relation of collinearity corresponds to the relation of linear dependence
of vectors. Several facts concerning vectors are proved, which correspond
in this language to some classical axioms of projective geometry.
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[2]
[10]
[3]
[5]
[4]
[1]
[6]
[9]
[8]
Contents (PDF format)
Bibliography
 [1]
Jozef Bialas.
Group and field definitions.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Beata Padlewska.
Families of sets.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Konrad Raczkowski and Pawel Sadowski.
Equivalence relations and classes of abstraction.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Wojciech Skaba.
The collinearity structure.
Journal of Formalized Mathematics,
2, 1990.
 [7]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [8]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
Received June 15, 1990
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