{"title":"Shape properties of the Stone-Čech compactification","authors":"James Keesling, R.B. Sher","doi":"10.1016/0016-660X(78)90037-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper it is shown that if <em>X</em> is a connected space which is not pesudocompact, then β<em>X</em> is not movable and does not have metric shape. In particular β<em>X</em> cannot have trivial shape. It is also shown that if <em>X</em> is Lindelöf and <em>KχβX</em>−<em>X</em> is a continuum, then <em>K</em> cannot be movable or have metric shape unless it is a point.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 1","pages":"Pages 1-8"},"PeriodicalIF":0.0000,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90037-5","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Topology and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0016660X78900375","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 12
Abstract
In this paper it is shown that if X is a connected space which is not pesudocompact, then βX is not movable and does not have metric shape. In particular βX cannot have trivial shape. It is also shown that if X is Lindelöf and KχβX−X is a continuum, then K cannot be movable or have metric shape unless it is a point.
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