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 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 of such that is the intersection of those closed half-spaces which support it at points of . This will be true for sets which are "small" relative to , where smallness can be measured in terms of dimension, density character, or -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