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.
Citation
Manoj Bhardwaj. Alexander V. Osipov. "Mildly version of Hurewicz basis covering property and Hurewicz measure zero spaces." Bull. Belg. Math. Soc. Simon Stevin 29 (1) 123 - 133, december 2022. https://doi.org/10.36045/j.bbms.210114a
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