{"title":"实现积空间的范畴代数的自同构","authors":"Dorothy Maharam","doi":"10.1016/0016-660X(79)90005-9","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>X</em> be an arbitrary product of separable complete metric spaces. It is proved that every automorphism of the “category algebra” (the Baire sets modulo first category sets) of <em>X</em> can be obtained from some one-to-one map <em>T</em> of <em>X</em> onto itself such that both <em>T</em> and <em>T</em><sup>−1</sup> preserve Baire sets and first category subsets of <em>X</em>.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 2","pages":"Pages 161-174"},"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)90005-9","citationCount":"5","resultStr":"{\"title\":\"Realizing automorphisms of category algebras of product spaces\",\"authors\":\"Dorothy Maharam\",\"doi\":\"10.1016/0016-660X(79)90005-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <em>X</em> be an arbitrary product of separable complete metric spaces. It is proved that every automorphism of the “category algebra” (the Baire sets modulo first category sets) of <em>X</em> can be obtained from some one-to-one map <em>T</em> of <em>X</em> onto itself such that both <em>T</em> and <em>T</em><sup>−1</sup> preserve Baire sets and first category subsets of <em>X</em>.</p></div>\",\"PeriodicalId\":100574,\"journal\":{\"name\":\"General Topology and its Applications\",\"volume\":\"10 2\",\"pages\":\"Pages 161-174\"},\"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)90005-9\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"General Topology and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0016660X79900059\",\"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/0016660X79900059","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Realizing automorphisms of category algebras of product spaces
Let X be an arbitrary product of separable complete metric spaces. It is proved that every automorphism of the “category algebra” (the Baire sets modulo first category sets) of X can be obtained from some one-to-one map T of X onto itself such that both T and T−1 preserve Baire sets and first category subsets of X.
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