{"title":"On bounded paradoxical sets and Lie groups","authors":"Grzegorz Tomkowicz","doi":"10.1007/s10711-024-00923-1","DOIUrl":null,"url":null,"abstract":"<p>We will prove that any non-empty open set in every complete connected metric space (<i>X</i>, <i>d</i>), where balls have compact closures, contains a paradoxical (uncountable) set relative to a non-supramenable connected Lie group that acts continuously and transitively on <i>X</i>.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10711-024-00923-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We will prove that any non-empty open set in every complete connected metric space (X, d), where balls have compact closures, contains a paradoxical (uncountable) set relative to a non-supramenable connected Lie group that acts continuously and transitively on X.
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