温和版本的Hurewicz基涵盖性质和Hurewicz测度零空间

Pub Date : 2022-02-25 DOI:10.36045/j.bbms.210114a
M. Bhardwaj, A. Osipov
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引用次数: 1

摘要

本文介绍了Babinkostova、Ko等研究的Hurewicz基覆盖性质的温和版本\v{c}伊纳克和舍普斯。一个空间 $X$ 对于每一个序列都有轻微的hurewicz性质 $\langle \mathcal{U}_n : n\in \omega \rangle$ 的打开的盖子的 $X$ 这是一个序列 $\langle \mathcal{V}_n : n\in \omega \rangle$ 这样对于每一个 $n$, $\mathcal{V}_n$ 的有限子集是 $\mathcal{U}_n$ 对于每一个 $x\in X$, $x$ 属于 $\bigcup\mathcal{V}_n$ 除了有限的一部分 $n$. 然后利用可度量空间的温和- hurewicz基性质和温和- hurewicz测度零性质来表征温和- hurewicz性质。
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Mildly version of Hurewicz basis covering property and Hurewicz measure zero spaces
In this paper, we introduced the mildly version of the Hurewicz basis covering property, studied by Babinkostova, Ko\v{c}inac, 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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