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Resolvable maps preserve complete metrizability
Author(s):
Su
Gao;
Vincent
Kieftenbeld
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2245-2252.
MSC (2010):
Primary 54E40, 54E50;
Secondary 03E15, 54H05
Posted:
February 1, 2010
MathSciNet review:
2596065
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Abstract:
Let  be a Polish space, let  be a separable metrizable space, and let  be a continuous surjection. We prove that if the image under  of every open set or every closed set is resolvable, then  is Polish. This generalizes similar results by Sierpiński, Vainštain, and Ostrovsky.
References:
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- 2.
- F. Hausdorff, Über innere Abbildungen, Fund. Math. 23 (1934), 279-291.
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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:
10.1090/S0002-9939-10-10246-9
PII:
S 0002-9939(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
Posted:
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 of article:
Copyright
2010,
American Mathematical Society
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