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Projective Geometries and Projective Lattices

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

Abstract

There exist many equivalent axiomatic characterizations of projective geometries. The first two sections of this chapter present two such possibilities. The first one uses the ternary relation collinear on the set of points. The second one works with the operator that associates to each couple of points a, b the line through a and ab and the singleton {a} if a = b. Another approach, by means of the closure operator C that associates to an arbitrary set A of points the subspace C(A) generated by A, will be studied in Chapter 3. The first section also includes a series of examples. The most important one is the projective geometry associated to an arbitrary vector space V. This geometry will be denoted by P(V). The points of P(V) are the one-dimensional vector subspaces of V, three of them being called collinear if they lie in a vector subspace of dimension ≤ 2.

Keywords

Irreducible Component Intersection Property Closure Operator Vector Space Versus Projective Geometry 
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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