Resolvable maps preserve complete metrizability

Gao, Su; Kieftenbeld, Vincent

doi:10.1090/S0002-9939-10-10246-9

Resolvable maps preserve complete metrizability
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by Su Gao and Vincent Kieftenbeld PDF

Proc. Amer. Math. Soc. 138 (2010), 2245-2252 Request permission

Abstract:

Let $X$ be a Polish space, let $Y$ be a separable metrizable space, and let $f \colon X \to Y$ be a continuous surjection. We prove that if the image under $f$ of every open set or every closed set is resolvable, then $Y$ is Polish. This generalizes similar results by Sierpiński, Vainštain, and Ostrovsky.

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