{"title":"Relationship between α-sets and weakly convex Vial sets","authors":"D. B. Davletov, A. Ershov, A. Ershova","doi":"10.32460/ISHMU-2020-8-0017","DOIUrl":null,"url":null,"abstract":"In the paper, we study properties of the α-sets, which are generalizations of the convex sets. Relationship between the α-sets and weakly convex sets is established. It is proved that the weakly convex Vial sets with bounded Chebyshev radius are α-ones. An example is given showing that the converse is not true.","PeriodicalId":154439,"journal":{"name":"VIII Information school of a young scientist Central Scientific Library of the Urals Branch of the Russian Academy of Science","volume":"18 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"VIII Information school of a young scientist Central Scientific Library of the Urals Branch of the Russian Academy of Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32460/ISHMU-2020-8-0017","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
In the paper, we study properties of the α-sets, which are generalizations of the convex sets. Relationship between the α-sets and weakly convex sets is established. It is proved that the weakly convex Vial sets with bounded Chebyshev radius are α-ones. An example is given showing that the converse is not true.
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