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Resolvable maps preserve complete metrizability


Authors: Su Gao and Vincent Kieftenbeld
Journal: Proc. Amer. Math. Soc. 138 (2010), 2245-2252
MSC (2010): Primary 54E40, 54E50; Secondary 03E15, 54H05
DOI: https://doi.org/10.1090/S0002-9939-10-10246-9
Published electronically: February 1, 2010
MathSciNet review: 2596065
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

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Additional Information

Su Gao
Affiliation: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, Texas 76203-5017
Email: sgao@unt.edu

Vincent Kieftenbeld
Affiliation: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, Texas 76203-5017
Email: kieftenbeld@unt.edu

DOI: https://doi.org/10.1090/S0002-9939-10-10246-9
Keywords: Complete metrizability, resolvable sets
Received by editor(s): July 15, 2009
Received by editor(s) in revised form: October 5, 2009
Published electronically: February 1, 2010
Additional Notes: The first author acknowledges the support of NSF grants DMS-0501039 and DMS-0901853.
The second author acknowledges the support of NSF grant DMS-0901853.
Communicated by: Julia Knight
Article copyright: © Copyright 2010 American Mathematical Society

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