Namioka spaces and topological games

Abstract

We introduce a class of $\beta-v$-unfavorable spaces, which contains some known classes of $\beta$-unfavorable spaces for topological games of Choquet type. It is proved that every $\beta-v$-unfavorable space $X$ is a Namioka space, that is for any compact space $Y$ and any separately continuous function $f:X\times Y\to \mathbb R$ there exists a dense in $X$ $G_{\delta}$-set $A\subseteq X$ such that $f$ is jointly continuous at each point of $A\times Y$.