{"title":"The Complement of a Closed Set Satisfying the Extended Exterior Sphere Condition","authors":"Chadi Nour, Jean Takche","doi":"arxiv-2407.20376","DOIUrl":null,"url":null,"abstract":"We provide a novel analytical proof of an improved version of [10, Theorem\n3.1], showing that the complement of a closed set satisfying the extended\nexterior sphere condition is nothing but the union of closed balls with lower\nsemicontinuous radius function. The improvement lies in the radius function,\nwhich is now larger than the one used in [10, Theorem 3.1].","PeriodicalId":501444,"journal":{"name":"arXiv - MATH - Metric Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Metric Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.20376","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We provide a novel analytical proof of an improved version of [10, Theorem
3.1], showing that the complement of a closed set satisfying the extended
exterior sphere condition is nothing but the union of closed balls with lower
semicontinuous radius function. The improvement lies in the radius function,
which is now larger than the one used in [10, Theorem 3.1].