  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 $x \in A$, $x \in {\rm St}(\cup
\mathcal{V}_n, \mathcal{U}_n)$ 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.
