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 language | English |
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Pages (from-to) | 243-257 |
Number of pages | 15 |
Journal | Discrete and Computational Geometry |
Volume | 38 |
Issue number | 2 |
DOIs | |
State | Published - 1 Jan 2007 |
Externally published | Yes |
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics