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.References
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Additional Information
- Su Gao
- Affiliation: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, Texas 76203-5017
- MR Author ID: 347662
- 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
- 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
- © Copyright 2010 American Mathematical Society
- 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
- MathSciNet review: 2596065