{"title":"Domain representable Lindelöf spaces are cofinally Polish","authors":"V. Tkachuk","doi":"10.1556/012.2019.56.4.1442","DOIUrl":null,"url":null,"abstract":"We prove that, for any cofinally Polish spaceX, every locally finite family of non-empty open subsets ofXis countable. It is also established that Lindelöf domain representable spaces are cofinally Polish and domain representability coincides with subcompactness in the class ofσ-compact spaces. It turns out that, for a topological groupGwhose space has the Lindelöf Σ-property, the spaceGis domain representable if and only if it is Čech-complete. Our results solve several published open questions.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1556/012.2019.56.4.1442","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We prove that, for any cofinally Polish spaceX, every locally finite family of non-empty open subsets ofXis countable. It is also established that Lindelöf domain representable spaces are cofinally Polish and domain representability coincides with subcompactness in the class ofσ-compact spaces. It turns out that, for a topological groupGwhose space has the Lindelöf Σ-property, the spaceGis domain representable if and only if it is Čech-complete. Our results solve several published open questions.
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