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Closure Spaces and Matroids

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

Abstract

Let G be a projective geometry. The associated closure operator C : P(G) → P(G) sends a subset AG to the smallest subspace of G which contains A. Given two points a, bG one has C({a,b}) = ab. Hence the closure operator C gives much more information than the operator ⋆ does, and it is therefore not surprising that a projective geometry can be described as a set G together with a closure operator C : P(G) → P(G) satisfying some additional axioms.

Keywords

Closed Subset Closure Operator Complete Lattice Projective Geometry Exchange Property 
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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