Continuity of separately continuous mappings. (English) Zbl 1349.54034

Mirmostafaee, Alireza Kamel

Math. Slovaca 64, No. 4, 1019-1026 (2014).

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

Keywords:

joint continuity; separate continuity; topological games; developable spaces