Hyperplanes that intersect each ray of a cone once and a Banach space counterexample (Q1669282)
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scientific article; zbMATH DE number 6929398
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hyperplanes that intersect each ray of a cone once and a Banach space counterexample |
scientific article; zbMATH DE number 6929398 |
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Hyperplanes that intersect each ray of a cone once and a Banach space counterexample (English)
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30 August 2018
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Summary: 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 \(C\, \backslash \{0 \}\) exactly once? We build on results found in [\textit{C. D. Aliprantis} and \textit{R. Tourky}, Cones and duality. Providence, RI: American Mathematical Society (AMS) (2007; Zbl 1127.46002)] and Klee jun.'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 \(C\, \backslash \{0 \}\) exactly once.
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