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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Pointwise compactness on extreme points


Author: Surjit Singh Khurana
Journal: Proc. Amer. Math. Soc. 83 (1981), 347-348
MSC: Primary 46A55; Secondary 52A07
DOI: https://doi.org/10.1090/S0002-9939-1981-0624928-0
MathSciNet review: 624928
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Abstract: It is proved that if $ X$ is a compact convex subset of a locally convex space $ E$, then the subset $ S$ of $ A$, the space of all affine, scalar-valued continuous functions on $ X$, which is uniformly bounded on $ X$ and relatively countably compact in the pointwise topology on $ {\text{ext}}(X)$, is relatively compact in the pointwise topology on $ X$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0624928-0
Keywords: Convex sets, barycenters, extreme points, integral representation
Article copyright: © Copyright 1981 American Mathematical Society