POINTS OF OPENNESS OF SOME MAPPINGS

Abstract

Let $X$ and $Y$ be topological spaces and $f: X \to Y$ be a continuous function. We are interested in finding points of $X$ and $Y$ at which $f$ is open.
We will show that if $X$ is developable, the set of points of openness of $f$ in $X$ is a $G_\delta$ subset of $X$.  If $X$ is developble and $f$ is closed, then the set of points of openness of $f$ in $Y$ is a $G_\delta$ subset of $Y$.  We will extend some results of S. Levi.