Separate and joint continuity. II
A function of two variables is called separately continuous if it is continuous with respect to each variable while the other one is fixed. This paper is a continuation of Part I, ibid. 11, 293-322 (1985; Zbl 0606.54009)]. There are presented some results, as well as open questions, connected to the problem of continuity of separately continuous functions defined on a product. Among others there are investigated Blumberg spaces, Sierpiński spaces and Namioka spaces which are the most interesting in this area. A space X is called to be the Namioka space whenever for every compact space Y and every metric space Z and every separately continuous function f from \(X\times Y\) into Z, there exist a dense \(G_{\delta}\)- set \(A\subset X\) such that f is continuous at every point of \(A\times Y\). There are pointed out some relationships between these classes of spaces.
continuity of separately continuous functions
scientific article; zbMATH DE number 4151346