Volume 2, 1990

University of Bialystok

Copyright (c) 1990 Association of Mizar Users

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

- With every affine space $A$ we correlate two incidence structures. The first, called Inc-ProjSp($A$), is the usual projective closure of $A$, i.e. the structure obtained from $A$ by adding directions of lines and planes of $A$. The second, called projective horizon of $A$, is the structure built from directions. We prove that Inc-ProjSp($A$) is always a projective space, and projective horizon of $A$ is a projective space provided $A$ is at least 3-dimensional. Some evident relationships between projective and affine configurational axioms that may hold in $A$ and in Inc-ProjSp($A$) are established.

Contents (PDF format)

- [1]
Czeslaw Bylinski.
Partial functions.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Wojciech Leonczuk, Henryk Oryszczyszyn, and Krzysztof Prazmowski.
Planes in affine spaces.
*Journal of Formalized Mathematics*, 2, 1990. - [4]
Wojciech Leonczuk and Krzysztof Prazmowski.
Incidence projective spaces.
*Journal of Formalized Mathematics*, 2, 1990. - [5]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Analytical ordered affine spaces.
*Journal of Formalized Mathematics*, 2, 1990. - [6]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Ordered affine spaces defined in terms of directed parallelity --- part I.
*Journal of Formalized Mathematics*, 2, 1990. - [7]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Parallelity and lines in affine spaces.
*Journal of Formalized Mathematics*, 2, 1990. - [8]
Konrad Raczkowski and Pawel Sadowski.
Equivalence relations and classes of abstraction.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [10]
Wojciech A. Trybulec.
Axioms of incidency.
*Journal of Formalized Mathematics*, 1, 1989. - [11]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [12]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989. - [14]
Edmund Woronowicz and Anna Zalewska.
Properties of binary relations.
*Journal of Formalized Mathematics*, 1, 1989.

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