A Construction of Analytical Projective Space

Wojciech Leonczuk

Warsaw University, Bialystok

Supported by RPBP.III-24.C6.

Krzysztof Prazmowski

Warsaw University, Bialystok

Supported by RPBP.III-24.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 non-zero 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.

MML Identifier: ANPROJ_1

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.