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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 C is a cone contained in real vector space V. When does V contain a hyperplane H that intersects each of the 0‐rays in C∖{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 C for which there does not exist a hyperplane that intersects each 0‐ray in C∖{0} exactly once.

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Handle: RePEc:wly:jnlaaa:v:2016:y:2016:i:1:n:9623090
DOI: 10.1155/2016/9623090
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