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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.
Received October 4, 2018, published March 29, 2019
Citation:
Alexander V. Osipov, “Remarks on Ostrovsky's theorem”, Sib. Èlektron. Mat. Izv., 16 (2019), 435–438
Linking options:
https://www.mathnet.ru/eng/semr1067 https://www.mathnet.ru/eng/semr/v16/p435
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Abstract page: | 251 | Full-text PDF : | 161 | References: | 21 |
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