{"title":"非阿基米德值函数的Bornological空间","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":"{\"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}","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}
Bornological spaces of non-Archimedean valued functions
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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