Metrizability of compact sets and continuous selections

Mägerl, G.

doi:10.1090/S0002-9939-1978-0509263-3

Metrizability of compact sets and continuous selections
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Proc. Amer. Math. Soc. 72 (1978), 607-612 Request permission

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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