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.
Chris McCarthy. "Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample." Abstr. Appl. Anal. 2016 1 - 7, 2016. https://doi.org/10.1155/2016/9623090