New basic result in classical descriptive set theory: preservation of completeness
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.
scientific article; zbMATH DE number 5558966