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Fall 1999 Dependent Choices and Weak Compactness
Christian Delhommé, Marianne Morillon
Notre Dame J. Formal Logic 40(4): 568-573 (Fall 1999). DOI: 10.1305/ndjfl/1012429720

Abstract

We work in set theory without the Axiom of Choice ZF. We prove that the Principle of Dependent Choices (DC) implies that the closed unit ball of a uniformly convex Banach space is weakly compact and, in particular, that the closed unit ball of a Hilbert space is weakly compact. These statements are not provable in ZF and the latter statement does not imply DC. Furthermore, DC does not imply that the closed unit ball of a reflexive space is weakly compact.

Citation

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Christian Delhommé. Marianne Morillon. "Dependent Choices and Weak Compactness." Notre Dame J. Formal Logic 40 (4) 568 - 573, Fall 1999. https://doi.org/10.1305/ndjfl/1012429720

Information

Published: Fall 1999
First available in Project Euclid: 30 January 2002

zbMATH: 0989.03048
MathSciNet: MR1858244
Digital Object Identifier: 10.1305/ndjfl/1012429720

Subjects:
Primary: 03E25
Secondary: 03E35

Rights: Copyright © 1999 University of Notre Dame

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Vol.40 • No. 4 • Fall 1999
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