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Proceedings of the American Mathematical Society

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Removable sets of support points of convex sets in Banach spaces

Author: R. R. Phelps
Journal: Proc. Amer. Math. Soc. 99 (1987), 319-322
MSC: Primary 46B20; Secondary 47D07, 52A07
MathSciNet review: 870793
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Abstract: A corollary of the Bishop-Phelps theorem is that a closed convex subset $C$ of a Banach space can always be represented as the intersection of its supporting closed half-spaces. In this paper an investigation is made of those subsets $S$ of $C$ such that $C$ is the intersection of those closed half-spaces which support it at points of $C\backslash S$. This will be true for sets $S$ which are "small" relative to $C$, where smallness can be measured in terms of dimension, density character, or $\sigma$-compactness.

References [Enhancements On Off] (What's this?)

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Keywords: Convex sets, Banach spaces, support points
Article copyright: © Copyright 1987 American Mathematical Society