{"title":"一维连续体超空间中的递归和熵","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":"{\"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}","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}
On recurrence and entropy in the hyperspace of continua in dimension one
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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