{"title":"温和版本的Hurewicz基涵盖性质和Hurewicz测度零空间","authors":"M. Bhardwaj, A. Osipov","doi":"10.36045/j.bbms.210114a","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":"7 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Mildly version of Hurewicz basis covering property and Hurewicz measure zero spaces\",\"authors\":\"M. Bhardwaj, A. Osipov\",\"doi\":\"10.36045/j.bbms.210114a\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":55309,\"journal\":{\"name\":\"Bulletin of the Belgian Mathematical Society-Simon Stevin\",\"volume\":\"7 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-02-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Belgian Mathematical Society-Simon Stevin\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.36045/j.bbms.210114a\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Belgian Mathematical Society-Simon Stevin","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.36045/j.bbms.210114a","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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