{"title":"全Assouad维度量子空间的一个刻画","authors":"Yoshito Ishiki","doi":"10.4171/jfg/109","DOIUrl":null,"url":null,"abstract":"We introduce the notion of tiling spaces for metric space. The class of tiling spaces includes the Euclidean spaces, the middle-third Cantor spaces, and various self-similar spaces appeared in fractal geometry. On a tiling space, we characterize a metric subspace whose Assouad dimension coincides with that of the whole space.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A characterization of metric subspaces of full Assouad dimension\",\"authors\":\"Yoshito Ishiki\",\"doi\":\"10.4171/jfg/109\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce the notion of tiling spaces for metric space. The class of tiling spaces includes the Euclidean spaces, the middle-third Cantor spaces, and various self-similar spaces appeared in fractal geometry. On a tiling space, we characterize a metric subspace whose Assouad dimension coincides with that of the whole space.\",\"PeriodicalId\":48484,\"journal\":{\"name\":\"Journal of Fractal Geometry\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2019-11-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Fractal Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/jfg/109\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Fractal Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jfg/109","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A characterization of metric subspaces of full Assouad dimension
We introduce the notion of tiling spaces for metric space. The class of tiling spaces includes the Euclidean spaces, the middle-third Cantor spaces, and various self-similar spaces appeared in fractal geometry. On a tiling space, we characterize a metric subspace whose Assouad dimension coincides with that of the whole space.
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