{"title":"拓扑空间的乘积","authors":"J.E. Vaughan","doi":"10.1016/0016-660X(78)90001-6","DOIUrl":null,"url":null,"abstract":"<div><p>The main purpose of this paper is to unify a number of theorems in topology whose conclusions state that a product of topological spaces has a compactness-like property.Three such theorems are (1) the Tychonoff theorem: Every product of compact spaces is compact, (2) the theorem of C.T. Scarborough and A.H. Stone: Every product of at most <strong>N</strong><sub>1</sub> sequentially compact spaces is countably compact, and (3) the theorem of N. Noble: A countable product of Lindelöf <em>P</em>-spaces is Lindelöf.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 3","pages":"Pages 207-217"},"PeriodicalIF":0.0000,"publicationDate":"1978-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90001-6","citationCount":"20","resultStr":"{\"title\":\"Products of topological spaces\",\"authors\":\"J.E. Vaughan\",\"doi\":\"10.1016/0016-660X(78)90001-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The main purpose of this paper is to unify a number of theorems in topology whose conclusions state that a product of topological spaces has a compactness-like property.Three such theorems are (1) the Tychonoff theorem: Every product of compact spaces is compact, (2) the theorem of C.T. Scarborough and A.H. Stone: Every product of at most <strong>N</strong><sub>1</sub> sequentially compact spaces is countably compact, and (3) the theorem of N. Noble: A countable product of Lindelöf <em>P</em>-spaces is Lindelöf.</p></div>\",\"PeriodicalId\":100574,\"journal\":{\"name\":\"General Topology and its Applications\",\"volume\":\"8 3\",\"pages\":\"Pages 207-217\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1978-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0016-660X(78)90001-6\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"General Topology and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0016660X78900016\",\"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/0016660X78900016","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The main purpose of this paper is to unify a number of theorems in topology whose conclusions state that a product of topological spaces has a compactness-like property.Three such theorems are (1) the Tychonoff theorem: Every product of compact spaces is compact, (2) the theorem of C.T. Scarborough and A.H. Stone: Every product of at most N1 sequentially compact spaces is countably compact, and (3) the theorem of N. Noble: A countable product of Lindelöf P-spaces is Lindelöf.
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