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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stable maps of Polish spaces


Author: A. V. Ostrovsky
Journal: Proc. Amer. Math. Soc. 128 (2000), 3081-3089
MSC (1991): Primary 54C10, 54D18
Published electronically: March 2, 2000
MathSciNet review: 1664430
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Abstract: We define the notions of stable and transquotient maps and study the relation between these classes of maps. The class of stable maps contains all closed and open maps and their compositions. The transquotient maps preserve the property of being a Polish space, and every stable map between separable metric spaces is transquotient.

In particular, a composition of closed and open maps (the intermediary spaces may not be metric) preserves the property of being a Polish space. This generalizes the results of Sierpinski and Vainstein for open and closed maps.


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Additional Information

A. V. Ostrovsky
Affiliation: EDV-Büro Wenninger, Schatzbogen 58, 81829 Muenchen, Germany
Email: ostrovsk@cip.mathematik.uni-muenchen.de

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05356-9
PII: S 0002-9939(00)05356-9
Keywords: Polish space, stable map, transquotient map, point--harmonious map
Received by editor(s): October 27, 1997
Received by editor(s) in revised form: November 5, 1998
Published electronically: March 2, 2000
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society