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Proceedings of the American Mathematical Society

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Total paracompactness and Banach spaces

Author: Francisco Gallego Lupiañez
Journal: Proc. Amer. Math. Soc. 103 (1988), 210-214
MSC: Primary 46B20; Secondary 54D18
MathSciNet review: 938670
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Abstract: In this paper, we study some problems related to the Corson theorem. In particular we prove that $ {c_0}$ does not fulfil such a theorem; hence this theorem is not valid for all infinite-dimensional Banach spaces. We give also generalizations of Corson's theorem for some infinite-dimensional normed spaces.

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Keywords: Open basis, locally finite covering, Banach spaces, bounded convex sets, normed spaces, total paracompactness
Article copyright: © Copyright 1988 American Mathematical Society