Convexity in Topological Affine Planes

We extend to topological affine planes the standard theorems of convexity, among them the separation theorem, the anti-exchange theorem, Radon’s, Helly’s, Carath´eodory’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. ¡ Supported in part by NSA grant H98230-05-1-0082 and PSC-CUNY grant 67018-0036. †Supported by The Research Council of Norway, project number 166618.

• Type: Journal
• Year: 2007
• Where: DCG
• Authors: Raghavan Dhandapani, Jacob E. Goodman, Andreas Holmsen, Richard Pollack, Shakhar Smorodinsky
• Keywords: Anti-exchange Theorem, DCG 2007, Minkowski Theorem, Standard Theorems