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

Authors

Chris McCarthy, CUNY Borough of Manhattan Community CollegeFollow

Document Type

Article

Publication Date

9-19-2016

Abstract

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.

Comments

This work was originally published in Abstract and Applied Sciences, available at doi:10.1155/2016/9623090.