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2015 Points of openness and closedness of some mappings
Lubica Holá, Alireza Kamel Mirmostafaee, Zbigniew Piotrowski
Banach J. Math. Anal. 9(1): 243-252 (2015). DOI: 10.15352/bjma/09-1-18

Abstract

Let $X$ and $Y$ be topological spaces and $f : X \rightarrow Y$ be a continuous function. We are interested in finding points of $Y$ at which $f$ is open or closed. We will show that under certain conditions, the set of points of openness or closedness of $f$ in $Y$ , i.e. points of $Y$ at which $f$ is open (resp. closed) is a $G_{\delta}$ subset of $Y$. We will extend some results of S. Levi, R. Engelking and I. A. Vaĭnšteĭn.

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Lubica Holá. Alireza Kamel Mirmostafaee. Zbigniew Piotrowski. "Points of openness and closedness of some mappings." Banach J. Math. Anal. 9 (1) 243 - 252, 2015. https://doi.org/10.15352/bjma/09-1-18

Information

Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1322.54010
MathSciNet: MR3296098
Digital Object Identifier: 10.15352/bjma/09-1-18

Subjects:
Primary: 46T20
Secondary: 47H04

Keywords: closed functions , Open functions , spaces with a base of countable order , ‎topological games

Rights: Copyright © 2015 Tusi Mathematical Research Group

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