{"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}
引用次数: 5
Abstract
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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