{"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}
引用次数: 20
Abstract
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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