{"title":"p-Adic nonconvex compactoids","authors":"W.H. Schikhof","doi":"10.1016/S1385-7258(89)80008-3","DOIUrl":null,"url":null,"abstract":"<div><p>A bounded subset <em>X</em> of a Banach space over a non-archimedean field ϰ is a compactoid if and only if each basic sequence in <em>X</em> tends to zero (Theorem 2). As a consequence the notions “weakly precompact’ and ‘precompact’ are identical for members of a wide class of ϰ-Banach spaces (Theorem 3).</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 3","pages":"Pages 339-342"},"PeriodicalIF":0.0000,"publicationDate":"1989-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80008-3","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725889800083","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
A bounded subset X of a Banach space over a non-archimedean field ϰ is a compactoid if and only if each basic sequence in X tends to zero (Theorem 2). As a consequence the notions “weakly precompact’ and ‘precompact’ are identical for members of a wide class of ϰ-Banach spaces (Theorem 3).
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