{"title":"Bornological spaces of non-Archimedean valued functions","authors":"A.K. Katsaras","doi":"10.1016/S1385-7258(87)80005-7","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>C(X,E)</em> be the space of all continuous functions from an ultraregular space <em>X</em> to a non-Archimedean locally convex space <em>E</em>. Necessary and/or sufficient conditions are given so that <em>C(X,E)</em>, with the topology of uniform convergence on compact sets or with the topology of simple convergence, is bornological or <em>c</em>-ultrabornological.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"90 1","pages":"Pages 41-50"},"PeriodicalIF":0.0000,"publicationDate":"1987-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(87)80005-7","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725887800057","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
Let C(X,E) be the space of all continuous functions from an ultraregular space X to a non-Archimedean locally convex space E. Necessary and/or sufficient conditions are given so that C(X,E), with the topology of uniform convergence on compact sets or with the topology of simple convergence, is bornological or c-ultrabornological.
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