2019
Том 71
№ 11

All Issues

Filipchuk O. I.

Articles: 2
Article (Ukrainian)

Discontinuity points of separately continuous mappings with at most countable set of values

Filipchuk O. I., Maslyuchenko V. K.

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 6. - pp. 801-807

UDC 517.51
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.

Article (Ukrainian)

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

Filipchuk O. I., Maslyuchenko V. K., Mykhailyuk V. V.

↓ Abstract   |   Full text (.pdf)

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 $y \in Y.$