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Continuity of separately continuous mappings. (English) Zbl 1349.54034
Summary: By means of a topological game, a class of topological spaces which contains compact spaces, \(q\)-spaces and \(W\)-spaces was defined in A. Bouziad [Topology Appl. 50, No. 1, 73–80 (1993; Zbl 0827.54018)]. We will show that if \(Y\) belongs to this class, every separately continuous function \(f\:X\times Y\to Z\) is jointly continuous on a dense subset of \(X \times Y\) provided that \(X\) is \(\sigma \)-\(\beta \)-unfavorable and \(Z\) is a regular weakly developable space.

MSC:
54C05 Continuous maps
54E30 Moore spaces
54E52 Baire category, Baire spaces
54C99 Maps and general types of topological spaces defined by maps
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