Topological games and strong quasi-continuity

Abstract

Let $X$ be a Baire space, $Y$ be a $W$-space and $Z$ be a regular topological space. We will show that every $KC$-function $f:X \times Y\to Z$ is strongly quasi-continuous at each point of $X \times Y$. In particular, when $X$ is a Baire space and $Y$ is Corson compact, every $KC$-function $f$ from $X \times Y$ to a Moore space $Z$ is jointly continuous on a dense subset of $X \times Y$. We also give a few applications of our results on continuity of group actions.