Filipchuk O. I.
Ukr. Mat. Zh. - 2019. - 71, № 6. - pp. 801-807
We obtain a general result on the constancy of separately continuous mappings and their analogs, which implies the wellknown Sierpi´nski theorem. By using this result, we study the set of continuity points of separately continuous mappings with at most countably many values including, in particular, the mappings defined on the square of the Sorgenfrey line with values in the Bing plane.
Ukr. Mat. Zh. - 2008. - 60, № 11. - pp. 1539 – 1547
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 $y \in Y.$