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ArticleOriginal scientific text

Title

Compactness and countable compactness in weak topologies

Authors 1

Affiliations

  1. Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, U.S.A.

Abstract

A bounded closed convex set K in a Banach space X is said to have quasi-normal structure if each bounded closed convex subset H of K for which diam(H) > 0 contains a point u for which ∥u-x∥ < diam(H) for each x ∈ H. It is shown that if the convex sets on the unit sphere in X satisfy this condition (which is much weaker than the assumption that convex sets on the unit sphere are separable), then relative to various weak topologies, the unit ball in X is compact whenever it is countably compact.

Keywords

ENG
weak topologies, compactness, countable compactness, quasi-normal structure, convexity structures

Bibliography

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Studia Mathematica
1994-1995/112/3
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Pages:
243-250
Main language of publication
English
Received
1993-09-15
Accepted
1994-03-02
Published
1995
Exact and natural sciences