{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-02-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.36045/j.bbms.210114a\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.36045/j.bbms.210114a","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","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.