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Hyperplanes That Intersect Each Ray Of A Cone Once And A Banach Space Counterexample, Chris Mccarthy
Hyperplanes That Intersect Each Ray Of A Cone Once And A Banach Space Counterexample, Chris Mccarthy
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Suppose � is a cone contained in real vector space �. When does � contain a hyperplane � that intersects each of the 0-rays in �\{0} exactly once? We build on results found in Aliprantis, Tourky, and Klee Jr.’s work to give a partial answer to this question.We also present an example of a salient, closed Banach space cone � for which there does not exist a hyperplane that intersects each 0-ray in � \ {0} exactly once.