Equi-cliquishness and the Hahn property

Abstract

We study the joint continuity of mappings of two variables. In particular, we show that for a Baire space $X$, a second countable space $Y$ and a metric space $Z$ a map $f:X\times Y \to Z$ has the Hahn property (i.e. there is a residual subset $A$ of $X$ such that $A\times Y\subseteq C(f)$) if and only if $f$ is locally equvi-cliquish with respect to $y$ and $\{x\in X: f^x \mbox{ is continuous}\}$ is a residual subset of $X$.