{"title":"Carathéodory completeness on the plane","authors":"A. Edigarian","doi":"10.4467/20843828am.19.002.12110","DOIUrl":null,"url":null,"abstract":". M. A. Selby [ 8–10 ] and, independently, N. Sibony [ 11 ] proved that on the complex plane c -completeness is equivalent to c -finitely com-pactness. Their proofs are quite similar and are based on [ 4 ]. We give more refined equivalent conditions and, along the way, simplify the proofs.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"1 1","pages":""},"PeriodicalIF":4.9000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4467/20843828am.19.002.12110","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
. M. A. Selby [ 8–10 ] and, independently, N. Sibony [ 11 ] proved that on the complex plane c -completeness is equivalent to c -finitely com-pactness. Their proofs are quite similar and are based on [ 4 ]. We give more refined equivalent conditions and, along the way, simplify the proofs.
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