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Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample

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  • Chris McCarthy

Abstract

Suppose is a cone contained in real vector space . When does contain a hyperplane that intersects each of the 0-rays in 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 exactly once.

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  • Chris McCarthy, 2016. "Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-7, October.
    • Handle: RePEc:hin:jnlaaa:9623090
    DOI: 10.1155/2016/9623090
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