Banach Journal of Mathematical Analysis

Points of openness and closedness of some mappings

Lubica Holá, Alireza Kamel Mirmostafaee, and Zbigniew Piotrowski

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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.

Article information

Banach J. Math. Anal., Volume 9, Number 1 (2015), 243-252.

First available in Project Euclid: 19 December 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46T20: Continuous and differentiable maps [See also 46G05]
Secondary: 47H04: Set-valued operators [See also 28B20, 54C60, 58C06]

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


Holá, Lubica; Kamel Mirmostafaee, Alireza; Piotrowski, Zbigniew. Points of openness and closedness of some mappings. Banach J. Math. Anal. 9 (2015), no. 1, 243--252. doi:10.15352/bjma/09-1-18.

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