温和版本的Hurewicz基涵盖性质和Hurewicz测度零空间

IF 0.4 4区 数学 Q4 MATHEMATICS
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
14
审稿时长
6-12 weeks
期刊介绍: The Bulletin of the Belgian Mathematical Society - Simon Stevin (BBMS) is a peer-reviewed journal devoted to recent developments in all areas in pure and applied mathematics. It is published as one yearly volume, containing five issues. The main focus lies on high level original research papers. They should aim to a broader mathematical audience in the sense that a well-written introduction is attractive to mathematicians outside the circle of experts in the subject, bringing motivation, background information, history and philosophy. The content has to be substantial enough: short one-small-result papers will not be taken into account in general, unless there are some particular arguments motivating publication, like an original point of view, a new short proof of a famous result etc. The BBMS also publishes expository papers that bring the state of the art of a current mainstream topic in mathematics. Here it is even more important that at leat a substantial part of the paper is accessible to a broader audience of mathematicians. The BBMS publishes papers in English, Dutch, French and German. All papers should have an abstract in English.
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