On weakly Hurewicz spaces

Abstract

A space $X$ is {\it weakly Hurewicz} if for each sequence
$(\mathcal U_n:n\in\Bbb N)$ of open covers of $X$, there are a
dense subset $Y\subseteq X$ and finite subfamilies $\mathcal
V_n\subseteq \mathcal U_n (n\in \Bbb N)$ such that for every point
of $Y$ is contained in $\bigcup\mathcal V_n$ for all but finitely
many $n$. In this paper, we investigate the relationship between
Hurewicz spaces and weakly Hurewicz spaces, and also study
topological properties of weakly Hurewicz spaces.