Convexity in topological affine planes

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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.
Publisher
SPRINGER
Issue Date
2007-09
Language
English
Article Type
Article
Keywords

ARRANGEMENTS

Citation

DISCRETE COMPUTATIONAL GEOMETRY, v.38, no.2, pp.243 - 257

ISSN
0179-5376
DOI
10.1007/s00454-007-1336-5
URI
http://hdl.handle.net/10203/88694
Appears in Collection
MA-Journal Papers(저널논문)
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