Joint continuity of $K_h C$-functions with values in moore spaces

Abstract

We introduce a notion of a categorical cliquish mapping and prove that, for each $K_h C$-mapping $f : X \times Y \rightarrow Z$ (here, $X$ is a topological space, $Y$ is a first countable space, and $Z$ is a Moore space) with categorical cliquish horizontal $y$-sections $f_y$ , the sets $C_y (f)$ are residual $G_\delta$-sets in $X$ for each $y \in Y.$