New basic result in classical descriptive set theory: preservation of completeness
type: Item
instance of: scholarly article
title: New basic result in classical descriptive set theory: preservation of completeness
zbMATH Open document ID: 1172.54019
author: Alexey Ostrovsky
published in: Topology and its Applications
publication date: 2009-05-28T00:00:00Z
review text: The author proves the following theorem: if \(X \subseteq \omega^{\omega}\) is completely metrizable and \(f : X \rightarrow Y\) is a continuous surjective function such that for every clopen set \(W \subseteq X\), \(f(W) = U \cup V\) where \(U\) is open and \(V\) is closed, then \(Y\) is also completely metrizable. This is a common generalization of results of \textit{W.\ Sierpiński} [Fundam. Math. 16, 173--180 (1930; JFM 56.0087.03)] and \textit{I. A. Vaĭnšteĭn} [On closed mappings, Moskov. Gos. Univ. Uč. Zap. Mat. 155 (5), 3--53, (1952)] which provide the same conclusion for open and closed maps, respectively.
reviewed by: Tamás Mátrai
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 03E15
Mathematics Subject Classification ID: 26A21
Mathematics Subject Classification ID: 54H05
zbMATH DE Number: 5558966
zbMATH Keywords: completely metrizable space
zbMATH Keywords: Borel space
zbMATH Keywords: open map
zbMATH Keywords: closed map
zbMATH Keywords: s-covering map
zbMATH Keywords: stable map
MaRDI profile type: Publication
full work available at URL: j.topol.2009.03.001
OpenAlex ID: W2055807929
cites work: On Closed Images of the Space of Irrationals
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DOI: 10.1016/J.TOPOL.2009.03.001
description: scientific article; zbMATH DE number 5558966