Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample
Copyright policy )Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample
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.
- King’s University United States
- THE CITY UNIVERSITY OF NEW YORK United States
QA1-939, Convex sets and cones of operators, Spaces of linear operators; topological tensor products; approximation properties, Convex sets in topological vector spaces (aspects of convex geometry), Mathematics
QA1-939, Convex sets and cones of operators, Spaces of linear operators; topological tensor products; approximation properties, Convex sets in topological vector spaces (aspects of convex geometry), Mathematics
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