Geodesic
On piecewise continuous mappings of paracompact spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 214-222

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It is proved that every resolvably measurable mapping $f \colon X \rightarrow Y$ of a first-countable perfectly paracompact space $X$ to a regular space $Y$ is piecewise continuous. If $X$ is additionally completely Baire, then $f$ is resolvably measurable if and only if it is piecewise continuous.
Keywords: resolvably measurable mapping, piecewise continuous mapping, $\mathcal{F}_\sigma$-measurable mapping, completely Baire space. 
@article{SEMR_2018_15_a43,
     author = {S. V. Medvedev},
     title = {On piecewise continuous mappings of paracompact spaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {214--222},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a43/}
}
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S. V. Medvedev. On piecewise continuous mappings of paracompact spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 214-222. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a43/