Stable maps of Polish spaces

Ostrovsky, A.

doi:10.1090/S0002-9939-00-05356-9

Stable maps of Polish spaces
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by A. V. Ostrovsky PDF

Proc. Amer. Math. Soc. 128 (2000), 3081-3089 Request permission

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 Sierpiński and Vainstein for open and closed maps.

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