{"title":"p-Adic非凸紧型","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":"{\"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}","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}
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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