{"title":"并不是所有的紧化Hausdorff空间都是超紧化的","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":"{\"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}","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
摘要
De Groot和Verbeek都要求给出一个紧凑的Hausdorff空间的例子它不是超紧凑的。如果X不是赝紧，那么βX就不是超紧。它是在更一般的沃尔曼紧化中完成的。
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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