A Projective Closure and Projective Horizon of an Affine Space

Henryk Oryszczyszyn

Warsaw University, Bialystok

Krzysztof Prazmowski

Warsaw University, Bialystok

Summary.

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.

MML Identifier: AFPROJ

Contents (PDF format)

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