Remarks on Ostrovsky's theorem

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-LCn function between Polish spaces piecewise open for n = 2, 3, ... ?) has a negative solution for each n > 1. © 2019 Osipov A.V.