On star-K-Hurewicz spaces

Yan-Kui Song

A space $X$ is \emph{star-K-Hurewicz} if for each sequence $(\mathcal U_n:n\in\mathbb N)$ of open covers of $X$ there exists a sequence $(K_n:n\in N)$ of compact subsets of $X$ such that for each $x\in X$, $x\in St(K_n,\mathcal U_n)$ for all but finitely many $n$. In this paper, we investigate the relationship between star-$K$-Hurewicz spaces and related spaces by giving some examples, and also study topological properties of star-$K$-Hurewicz spaces.