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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
DOI: https://doi.org/10.1090/S0002-9939-1987-0870793-1
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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0870793-1
Keywords: Convex sets, Banach spaces, support points
Article copyright: © Copyright 1987 American Mathematical Society