Convexity in Topological Affine Planes |
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| Authors: | Raghavan Dhandapani Jacob E Goodman Andreas Holmsen Richard Pollack Shakhar Smorodinsky |
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| Institution: | (1) Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA;(2) Department of Mathematics, City College, CUNY, New York, NY 10031, USA;(3) Department of Mathematics, University of Bergen, 5008 Bergen, Norway |
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| 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. |
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