Convexity in Topological Affine Planes
نویسندگان
چکیده
We extend to topological affine planes the standard theorems of convexity, among them the separation theorem, the anti-exchange theorem, Radon’s, Helly’s, Carathéodory’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. ‡Supported in part by NSF grant CCR-9732101.
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عنوان ژورنال:
- Discrete & Computational Geometry
دوره 38 شماره
صفحات -
تاریخ انتشار 2007