{"title":"区间度量空间的完备性","authors":"Rukhsar Khatun, Md Sadikur Rahman, Amar Kumar Banerjee, Asoke Kumar Bhunia","doi":"10.1007/s13370-024-01200-w","DOIUrl":null,"url":null,"abstract":"<div><p>The purpose of this paper is to study the completeness properties of interval metric spaces. The idea of convergence and Cauchyness of sequences with respect to an interval metric are studied to introduce the notions of <i>i</i>-convergent and <i>i</i>-Cauchy sequences respectively. Several relevant results including relations between convergent and <i>i</i>-convergent sequences, Cauchy and <i>i</i>-Cauchy sequences are established. A characterization for completeness of an interval metric space is given in terms of completeness of metric spaces.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 3","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Completeness properties of interval metric spaces\",\"authors\":\"Rukhsar Khatun, Md Sadikur Rahman, Amar Kumar Banerjee, Asoke Kumar Bhunia\",\"doi\":\"10.1007/s13370-024-01200-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The purpose of this paper is to study the completeness properties of interval metric spaces. The idea of convergence and Cauchyness of sequences with respect to an interval metric are studied to introduce the notions of <i>i</i>-convergent and <i>i</i>-Cauchy sequences respectively. Several relevant results including relations between convergent and <i>i</i>-convergent sequences, Cauchy and <i>i</i>-Cauchy sequences are established. A characterization for completeness of an interval metric space is given in terms of completeness of metric spaces.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"35 3\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-024-01200-w\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-024-01200-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
The purpose of this paper is to study the completeness properties of interval metric spaces. The idea of convergence and Cauchyness of sequences with respect to an interval metric are studied to introduce the notions of i-convergent and i-Cauchy sequences respectively. Several relevant results including relations between convergent and i-convergent sequences, Cauchy and i-Cauchy sequences are established. A characterization for completeness of an interval metric space is given in terms of completeness of metric spaces.
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