On H1-compositors and piecewise continuous mappings (in Ukrainian)

Author O. O. Karlova, O. V. Sobchuk

Abstract 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 $f\colon X\to Y$ 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.
Keywords right $H_1$-compositor; right $B_1$-compositor; mapping of the first Lebesgue class; $G_\delta$-measurable mapping; piecewise continuous mapping; $k$-continuous mapping; weakly $k$-continuous mapping
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Pages 139-146
Volume 38
Issue 2
Year 2012
Journal Matematychni Studii
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