Hurewicz

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A regular space is called a Hurewicz space if and only if for each sequence of open coverings $Y_1,Y_2,\ldots$ there exist finite subcollections $\mathcal{A}_i$ of $Y_i$ such that $\mathcal{A}_1 \cup \mathcal{A_2} \cup \ldots$ is a covering.

See Also

Strongly Hurewicz