Geodesic
Remarks on Ostrovsky's theorem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 435-438

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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. 
@article{SEMR_2019_16_a51,
     author = {Alexander V. Osipov},
     title = {Remarks on {Ostrovsky's} theorem},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {435--438},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a51/}
}
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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/