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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 214–222 (Mi semr912)  

Geometry and topology

On piecewise continuous mappings of paracompact spaces

S. V. Medvedevab

a Department of Mathematical Analysis and Methods of Teaching Mathematics, South Ural State University, pr. Lenina, 76, 454080, Chelyabinsk, Russia
b Krasovskii Institute of Mathematics and Mechanics of UB RAS, Russia

Abstract: 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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 02.A03.21.0011
The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0011.


DOI: https://doi.org/10.17377/semi.2018.15.021

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Bibliographic databases:

Document Type: Article
UDC: 515.126
MSC: 54C08, 54E52
Received October 22, 2017, published March 13, 2018
Language: English

Citation: S. V. Medvedev, “On piecewise continuous mappings of paracompact spaces”, Sib. Èlektron. Mat. Izv., 15 (2018), 214–222

Citation in format AMSBIB
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\by S.~V.~Medvedev
\paper On piecewise continuous mappings of paracompact spaces
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 214--222
\mathnet{http://mi.mathnet.ru/semr912}
\crossref{https://doi.org/10.17377/semi.2018.15.021}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438412200021}


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