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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Topologies of pointwise convergence on families of extremal points and weak compactness


Author: Ian Tweddle
Journal: Proc. Amer. Math. Soc. 86 (1982), 85-86
MSC: Primary 46A05
MathSciNet review: 663872
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Abstract: Bourgain and Talagrand showed that a bounded subset of a Banach space is weakly relatively compact provided it is relatively countably compact for the topology of pointwise convergence on the extremal points of the closed unit ball in the dual space. We give a version of this result for quasi-complete locally convex spaces. We also consider situations where the completeness or boundedness assumptions may be relaxed.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0663872-0
PII: S 0002-9939(1982)0663872-0
Article copyright: © Copyright 1982 American Mathematical Society