Abstract
In this paper, we introduced the mildly version of the Hurewicz basis covering property, studied by Babinkostova, Kočinac, and Scheepers. A space $X$ is said to have mildly-Hurewicz property if for each sequence $\langle\mathcal{U}_n : n \in \omega \rangle$ of clopen covers of $X$ there is a sequence $\langle \mathcal{V}_n : n \in \omega \rangle$ such that for each $n$, $\mathcal{V}_n$ is a finite subset of $\mathcal{U}_n$ and for each $x \in X$, $x$ belongs to $\bigcup \mathcal{V}_n$ for all but finitely many $n$. Then we characterized mildly-Hurewicz property by mildly-Hurewicz Basis property and mildly-Hurewicz measure zero property for metrizable spaces.
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More From: Bulletin of the Belgian Mathematical Society - Simon Stevin
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