On $H_1$-compositors and piecewise continuous mappings (in Ukrainian)

We introduce the notion of a right $H_1$-compositor and prove that for a hereditarily Baire metrizable space $X$, a normal space $Y$ and a mapping $fcolon Xto Y$ the following conditions are equivalent: (i) $f$ is piecewise continuous; (ii) $f$ is $k$-continuous; (iii) $f$ is $G_delta$-measurable; if, moreover, $Y$ is perfect, then (i)--(iii) are equivalent to: (iv) $f$ is a right $H_1$-compositor.