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Matematychni Studii 2012
On H1-compositors and piecewise continuous mappings (in Ukrainian)Keywords: right H 1 -compositor , right B 1 -compositor , mapping of the first Lebesgue class , G δ -measurable mapping , piecewise continuous mapping , k -continuous mapping , weakly k -continuous mapping Abstract: We introduce the notion of a right $H_1$-compositor and provethat for a hereditarily Baire metrizable space $X$, a normalspace $Y$ and a mapping $fcolon Xo Y$ the followingconditions 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 equivalentto: (iv) $f$ is a right $H_1$-compositor.
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