{"title":"Every Polish group has a non-trivial topological group automorphism","authors":"Carlos Pérez Estrada, Ulises Ariet Ramos-García","doi":"arxiv-2408.16162","DOIUrl":null,"url":null,"abstract":"We prove that every Polish group admits a non-trivial topological group\nautomorphism. This answers a question posed by Forte Shinko. As a consequence,\nwe prove that there are no uniquely homogeneous Polish groups.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":"45 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.16162","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 prove that every Polish group admits a non-trivial topological group
automorphism. This answers a question posed by Forte Shinko. As a consequence,
we prove that there are no uniquely homogeneous Polish groups.
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