Banach Journal of Mathematical Analysis, ( ISI ), Volume (9), No (1), Year (2015-1) , Pages (243-252)

#### Title : ( Points of openness and closedness of some mappings )

Authors: Lubica Hola , Seyyed Alireza Kamel Mirmostafaee , Z. Piotrowski ,

Citation: BibTeX | EndNote

#### Abstract

Let $X$ and $Y$ be topological spaces and $f:X \to Y$ 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. Va\u{\i}n\v{s}te\u{\i}n.

#### Keywords

, pen functions, closed functions, spaces with a base of countable order, topological games.
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@article{paperid:1041211,
author = {Lubica Hola and Kamel Mirmostafaee, Seyyed Alireza and Z. Piotrowski},
title = {Points of openness and closedness of some mappings},
journal = {Banach Journal of Mathematical Analysis},
year = {2015},
volume = {9},
number = {1},
month = {January},
issn = {1735-8787},
pages = {243--252},
numpages = {9},
keywords = {pen functions; closed functions; spaces with a base of countable order; topological games.},
}