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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - S. V. Medvedev
TI  - On piecewise continuous mappings of paracompact spaces
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 214
EP  - 222
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a43/
LA  - en
ID  - SEMR_2018_15_a43
ER  - 
%0 Journal Article
%A S. V. Medvedev
%T On piecewise continuous mappings of paracompact spaces
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 214-222
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a43/
%G en
%F SEMR_2018_15_a43
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/

[1] T. Banakh, B. Bokalo, “On scatteredly continuous maps between topological spaces”, Topology Appl., 157:1 (2010), 108–122 | DOI | MR

[2] T. Banakh, B. Bokalo, “Weakly discontinuous and resolvable functions between topological spaces”, Hacet. J. Math. Stat., 46:1 (2017), 103–110 | MR

[3] E.K. van Douwen, “Closed copies of rationals”, Comment. Math. Univ. Carolin., 28:1 (1987), 137–139 | MR

[4] R. Engelking, General topology, PWN, Warszawa, 1977 | MR

[5] J. E. Jayne, C. A. Rogers, “First level Borel functions and isomorphisms”, J. Math. Pures Appl., 61 (1982), 177–205 | MR

[6] W. Hurewicz, “Relativ perfekte Teile von Punktmengen und Mengen (A)”, Fund. Math., 12 (1928), 78–109 | DOI | Zbl

[7] M. Kačena, L. Motto Ros, B. Semmes, “Some observations on “A new proof of a theorem of Jayne and Rogers””, Real Analysis Exchange, 38:1 (2012/2013), 121–132 | MR

[8] K. Kuratowski, Topology, v. 1, PWN, Warszawa, 1966 | MR

[9] Mosc. Univ. Math. Bull., 41:2 (1986), 62–65 | MR | Zbl

[10] A. Ostrovsky, “Luzin's topological problem”, Topology Appl., 230 (2017), 45–50 | DOI | MR

[11] S. Solecki, “Decomposing Borel sets and functions and the structure of Baire class 1 functions”, J. Amer. Math. Soc., 11:3 (1998), 521–550 | DOI | MR

[12] A.H. Stone, “Kernel construction and Borel sets”, Trans. Amer. Math. Soc., 107 (1963), 58–70 | DOI | MR

[13] V.A. Vinokurov, “Strong regularizability of discontinuous functions”, Dokl. Akad. Nauk SSSR, 281:2 (1985), 265–269 (in Russian) | MR