Baire and weakly Namioka spaces (Q452094)

A Hausdorff space \(X\) is weakly Namioka if for every second countable space \(Y\) and every metric space \(Z\), every separately continuous function \(f \) from the product \(X \times Y\) into \(Z\) is continuous on \(D \times Y\) for some dense \(G_{\delta}\) subset \(D\) of \(X\). The main result of this paper states that: In the class of all completely regular separable spaces and in the class of all perfectly normal spaces, \(X\) is Baire if and only if it is weakly Namioka.