Points of openness and closedness of some mappings

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.