Geodesic
Remarks on Ostrovsky's theorem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 435-438 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Remarks on {Ostrovsky's} theorem},
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Alexander V. Osipov. Remarks on Ostrovsky's theorem. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 435-438. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a51/

[1] K. Kuratovski, Topology, v. I, Academic Press, 1966 | MR

[2] L. Motto Ros, B. Semmes, “A New Proof of a Theorem of Jayne and Rogers”, Real Analysis Exchange, 35:1 (2009), 195–204 | MR

[3] J. Jayne, C. Rogers, “First level Borel functions and isomorphisms”, J. Math. pures et appl., 61 (1982), 177–205 | MR | Zbl

[4] A. Ostrovsky, “Open-constructible functions”, Topology Appl., 178 (2014), 453–458 | DOI | MR | Zbl

[5] A. Ostrovsky, “Generalization of sequences and convergence in metric spaces”, Topology Appl., 171 (2014), 63–70 | DOI | MR | Zbl

[6] A. Ostrovsky, $LC_n$-measurable functions, Conference Paper, 2014