Star versions of Hurewicz spaces

Abstract

A space $X$ is said to have the set star Hurewicz property if for each nonempty subset $A$ of $X$ and each sequence $({\mathcal{U}}_n:n\in \mathbb{N})$ of sets open in $X$ such that for each $n\in \mathbb{N}$, $\overline{A}\subset \cup {\mathcal{U}}_n$, there is a sequence $({\mathcal{V}}_n:n\in \mathbb{N})$ such that for each $n\in \mathbb{N}$, ${\mathcal{V}}_n$ is a finite subset of ${\mathcal{U}}_n$ and for each $x\in A$, $x\in \mathrm{St}(\cup {\mathcal{V}}_n,{\mathcal{U}}_n)$ for all but finitely many $n$. In this paper, we investigate the relationships among set star Hurewicz, set strongly star Hurewicz and other related covering properties and study the topological properties of these topological spaces.

11 pages; Comments are welcome