Convexity in topological affine planes

Raghavan Dhandapani, Jacob E. Goodman, Andreas Holmsen, Richard Pollack, Shakhar Smorodinsky

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We extend to topological affine planes the standard theorems of convexity, among them the separation theorem, the anti-exchange theorem, Radon's, Helly's, Caratheodory's, and Kirchberger's theorems, and the Minkowski theorem on extreme points. In a few cases the proofs are obtained by adapting proofs of the original results in the Euclidean plane; in others it is necessary to devise new proofs that are valid in the more general setting considered here.

Original languageEnglish
Pages (from-to)243-257
Number of pages15
JournalDiscrete and Computational Geometry
Volume38
Issue number2
DOIs
StatePublished - 1 Jan 2007
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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