{"title":"The Lelek fan admits a completely scrambled weakly mixing homeomorphism","authors":"Piotr Oprocha","doi":"10.1112/blms.13205","DOIUrl":null,"url":null,"abstract":"<p>We prove that the Lelek fan admits a completely scrambled weakly mixing homeomorphism. This is then used to show that for every <span></span><math>\n <semantics>\n <mi>n</mi>\n <annotation>$n$</annotation>\n </semantics></math> there is a continuum of topological dimension <span></span><math>\n <semantics>\n <mi>n</mi>\n <annotation>$n$</annotation>\n </semantics></math> admitting a weakly mixing completely scrambled homeomorphism. This provides a final answer to a question from 2001.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"432-443"},"PeriodicalIF":0.8000,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13205","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13205","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that the Lelek fan admits a completely scrambled weakly mixing homeomorphism. This is then used to show that for every there is a continuum of topological dimension admitting a weakly mixing completely scrambled homeomorphism. This provides a final answer to a question from 2001.
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