Removable sets of support points of convex sets in Banach spaces
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- by R. R. Phelps PDF
- Proc. Amer. Math. Soc. 99 (1987), 319-322 Request permission
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
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Additional Information
- © Copyright 1987 American Mathematical Society
- 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