{"title":"Not all compact Hausdorff spaces are supercompact","authors":"Murray G. Bell","doi":"10.1016/0016-660X(78)90046-6","DOIUrl":null,"url":null,"abstract":"<div><p>De Groot and Verbeek have both asked for an example of a compact Hausdorff space which is not supercompact. Is is shown here that if <em>X</em> is not pseudocompact, then β<em>X</em> is not supercompact. It is done in the more general setting of Wallman compactifications.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 2","pages":"Pages 151-155"},"PeriodicalIF":0.0000,"publicationDate":"1978-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90046-6","citationCount":"14","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Topology and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0016660X78900466","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 14
Abstract
De Groot and Verbeek have both asked for an example of a compact Hausdorff space which is not supercompact. Is is shown here that if X is not pseudocompact, then βX is not supercompact. It is done in the more general setting of Wallman compactifications.
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