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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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