Remarks on star-K-Menger spaces

Abstract

A space $X$ is {\it star-K-Menger} if for each sequence $(\mathcal U_n:n\in\Bbb N)$ of open covers of $X$ there exists a sequence $(K_n:n\in N)$ of compact subsets of $X$ such that $\{St(K_n,\mathcal U_n):n\in\Bbb N\}$ is an open cover of $X$. In this paper, we construct an example of a Hausdorff star-Menger space that is not star-K-Menger which gives an answer to a question of Song [12], and continue to investigate topological properties of star-K-Menger spaces.