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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 435–438 (Mi semr1067)  

Geometry and topology

Remarks on Ostrovsky's theorem

Alexander V. Osipovabc

a Krasovskii Institute of Mathematics and Mechanics, 16, S.Kovalevskay str., Yekaterinburg, 620990, Russia
b Ural State University of Economics
c Ural Federal University

Abstract: In this paper we prove that the condition 'one-to-one' of the continuous open-resolvable mapping is necessary in the Ostrovsky theorem (Theorem 1 in [4]). Also we get that the Ostrovsky problem ([6], Problem 2) (Is every continuous open-$LC_n$ function between Polish spaces piecewise open for $n=2,3,...$ ?) has a negative solution for each $n>1$.

Keywords: open-resolvable function, open function, resolvable set, open-$LC_n$ function, piecewise open function, scatteredly open function.

DOI: https://doi.org/10.33048/semi.2019.16.025

Full text: PDF file (126 kB)
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Bibliographic databases:

Document Type: Article
UDC: 515.126, 515.124, 515.128
MSC: 26A15, 54C08, 26A21, 54H05, 54E40
Received October 4, 2018, published March 29, 2019
Language: English

Citation: Alexander V. Osipov, “Remarks on Ostrovsky's theorem”, Sib. Èlektron. Mat. Izv., 16 (2019), 435–438

Citation in format AMSBIB
\Bibitem{Osi19}
\by Alexander~V.~Osipov
\paper Remarks on Ostrovsky's theorem
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 435--438
\mathnet{http://mi.mathnet.ru/semr1067}
\crossref{https://doi.org/10.33048/semi.2019.16.025}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000462734100003}


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