{"title":"紧空间的逆极限","authors":"A.H. Stone","doi":"10.1016/0016-660X(79)90008-4","DOIUrl":null,"url":null,"abstract":"<div><p>This paper gives conditions under which the inverse limit of a system of compact (but non-Hausdorff) spaces will be non-empty, or compact, or hereditarily compact. The main result (Theorems 3 and 5) is that, if the spaces are compact, <em>T</em><sub>0</sub> and non-empty and the maps are closed and continuous, then the inverse limit is compact and non-empty (and, trivially, <em>T</em><sub>0</sub>). Simple examples are given to show that the results are reasonably sharp.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 2","pages":"Pages 203-211"},"PeriodicalIF":0.0000,"publicationDate":"1979-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90008-4","citationCount":"30","resultStr":"{\"title\":\"Inverse limits of compact spaces\",\"authors\":\"A.H. Stone\",\"doi\":\"10.1016/0016-660X(79)90008-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper gives conditions under which the inverse limit of a system of compact (but non-Hausdorff) spaces will be non-empty, or compact, or hereditarily compact. The main result (Theorems 3 and 5) is that, if the spaces are compact, <em>T</em><sub>0</sub> and non-empty and the maps are closed and continuous, then the inverse limit is compact and non-empty (and, trivially, <em>T</em><sub>0</sub>). Simple examples are given to show that the results are reasonably sharp.</p></div>\",\"PeriodicalId\":100574,\"journal\":{\"name\":\"General Topology and its Applications\",\"volume\":\"10 2\",\"pages\":\"Pages 203-211\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1979-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0016-660X(79)90008-4\",\"citationCount\":\"30\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"General Topology and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0016660X79900084\",\"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/0016660X79900084","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper gives conditions under which the inverse limit of a system of compact (but non-Hausdorff) spaces will be non-empty, or compact, or hereditarily compact. The main result (Theorems 3 and 5) is that, if the spaces are compact, T0 and non-empty and the maps are closed and continuous, then the inverse limit is compact and non-empty (and, trivially, T0). Simple examples are given to show that the results are reasonably sharp.
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