{"title":"An asymptotic extension of Moran construction in metric measure spaces","authors":"Da Wu","doi":"10.21099/tkbjm/1461270054","DOIUrl":null,"url":null,"abstract":". In this paper, we define asymptotically generalized Cantor sets in metric measure spaces by generalizing the notion of l -similarity maps. We define the notion of ð l ; c ; n Þ -similarity maps, and extend the Moran theorem about the generalized Cantor set in R d to this general setting. As an example, we construct generalized Cantor sets in Riemannian manifolds by using ð l ; c ; n Þ -similarity maps.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.21099/tkbjm/1461270054","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsukuba Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21099/tkbjm/1461270054","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
. In this paper, we define asymptotically generalized Cantor sets in metric measure spaces by generalizing the notion of l -similarity maps. We define the notion of ð l ; c ; n Þ -similarity maps, and extend the Moran theorem about the generalized Cantor set in R d to this general setting. As an example, we construct generalized Cantor sets in Riemannian manifolds by using ð l ; c ; n Þ -similarity maps.