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Morphisms of Projective Geometries

  • Claude-Alain Faure
  • Alfred Frölicher
Chapter
  • 575 Downloads
Part of the Mathematics and Its Applications book series (MAIA, volume 521)

Abstract

Since a morphism from a projective geometry G 1 to another one G 2 is a map that is defined on certain, but in general not on all points of G 1, we begin the chapter with some generalities on the so-called partial maps. A partial map from a set X to a set Y, noted f: X - -→ Y,is a map f from a subset of X, called the domain of f,to Y. The points of X which are not in the domain of f form the so-called kernel of f. The sets together with the partial maps form a category Par. In the first section we give some elementary basic facts concerning this category. One can avoid partial maps by working with the equivalent category Set* of pointed sets. This is sometimes quite useful, but it involves that one has to add to the points of every projective geometry an additional point which can be considered as the zero element of the lattice of subspaces, but has no direct geometric interpretation.

Keywords

Vector Space Irreducible Component Projective Geometry Canonical Projection Vector Subspace 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Claude-Alain Faure
    • 1
  • Alfred Frölicher
    • 1
  1. 1.University of GenevaGenevaSwitzerland

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