Convexity in Topological Affine Planes

被引：0
|
作者：
Raghavan Dhandapani
Jacob E. Goodman
Andreas Holmsen
Richard Pollack
Shakhar Smorodinsky
机构：
[1] Courant Institute,
[2] NYU,undefined
[3] 251 Mercer St.,undefined
[4] Department of Mathematics,undefined
[5] City College,undefined
[6] CUNY,undefined
[7] Department of Mathematics,undefined
[8] University of Bergen,undefined
来源：
Discrete & Computational Geometry | 2007年 / 38卷
关键词：
Discrete Comput Geom; Euclidean Plane; Separation Theorem; Antipodal Point; Pseudoline Arrangement;
D O I：
暂无
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学科分类号：
摘要：
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.
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页码：243 / 257
页数：14
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