# Strongly Hurewicz

A regular space is called a strongly Hurewicz space if and only if for each sequence of open coverings $Y_1, Y_2, \ldots$ of $X$, there exist finite subcollections $\mathcal{A}_i$ of $Y_i$ such that $X$ is the union over $i$ of the intersection over $j$ of $\mathcal{A}_{i+j}^*$. The $*$ notation is defined as follows: if $G$ is a collection of sets, then $G^*$ denotes the sum of all the sets in $G$.