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

Metrizability of compact sets and continuous selections


Author: G. Mägerl
Journal: Proc. Amer. Math. Soc. 72 (1978), 607-612
MSC: Primary 54C65; Secondary 46A99
MathSciNet review: 509263
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Abstract: It is shown that, in two of Michael's theorems on continuous selections, the condition that the range of the correspondence under consideration be metrizable is not only essential (as known through several counterexamples), but in some sense also necessary. This yields a characterization of metrizability for compact spaces and compact convex sets by means of continuous selections.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0509263-3
PII: S 0002-9939(1978)0509263-3
Keywords: Continuous selections, metrizability of compact sets
Article copyright: © Copyright 1978 American Mathematical Society