{"title":"On recurrence and entropy in the hyperspace of continua in dimension one","authors":"Domagoj Jelić, Piotr Oprocha","doi":"10.4064/fm235-4-2023","DOIUrl":null,"url":null,"abstract":"We show that if $G$ is a topological graph, and $f\\colon G\\to G$ is a continuous map, then the induced map $\\tilde {f}$ defined on the hyperspace $C(G)$ of all connected subsets of $G$ by the natural formula $\\tilde {f}(C)=f(C)$ carries the same entro","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":"20 1","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamenta Mathematicae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4064/fm235-4-2023","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We show that if $G$ is a topological graph, and $f\colon G\to G$ is a continuous map, then the induced map $\tilde {f}$ defined on the hyperspace $C(G)$ of all connected subsets of $G$ by the natural formula $\tilde {f}(C)=f(C)$ carries the same entro
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FUNDAMENTA MATHEMATICAE concentrates on papers devoted to
Set Theory,
Mathematical Logic and Foundations of Mathematics,
Topology and its Interactions with Algebra,
Dynamical Systems.
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