{"title":"扩展和改进锥形二梳齿","authors":"Giuliano Basso","doi":"10.4171/LEM/1043","DOIUrl":null,"url":null,"abstract":"We prove that for every reversible conical bicombing $\\sigma$ on a metric space $X$, there exists a conical bicombing on the injective hull of $X$ that extends $\\sigma$. We also establish a Descombes-Lang type result stating that every proper metric space with a conical bicombing admits a consistent bicombing satisfying certain convexity conditions.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"6 6","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Extending and improving conical bicombings\",\"authors\":\"Giuliano Basso\",\"doi\":\"10.4171/LEM/1043\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that for every reversible conical bicombing $\\\\sigma$ on a metric space $X$, there exists a conical bicombing on the injective hull of $X$ that extends $\\\\sigma$. We also establish a Descombes-Lang type result stating that every proper metric space with a conical bicombing admits a consistent bicombing satisfying certain convexity conditions.\",\"PeriodicalId\":344085,\"journal\":{\"name\":\"L’Enseignement Mathématique\",\"volume\":\"6 6\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"L’Enseignement Mathématique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/LEM/1043\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"L’Enseignement Mathématique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/LEM/1043","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove that for every reversible conical bicombing $\sigma$ on a metric space $X$, there exists a conical bicombing on the injective hull of $X$ that extends $\sigma$. We also establish a Descombes-Lang type result stating that every proper metric space with a conical bicombing admits a consistent bicombing satisfying certain convexity conditions.
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