{"title":"局部拟凸收敛群的对偶性","authors":"Pranav Sharma","doi":"10.4995/AGT.2021.14585","DOIUrl":null,"url":null,"abstract":"In the realm of the convergence spaces, the generalisation of topological groups is the convergence groups, and the corresponding extension of the Pontryagin duality is the continuous duality. We prove that local quasi-convexity is a necessary condition for a convergence group to be creflexive. Further, we prove that every character group of a convergence group is locally quasi-convex. 2010 MSC: 43A40; 54A20; 54H11.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"31 1","pages":"193"},"PeriodicalIF":0.6000,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Duality of locally quasi-convex convergence groups\",\"authors\":\"Pranav Sharma\",\"doi\":\"10.4995/AGT.2021.14585\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the realm of the convergence spaces, the generalisation of topological groups is the convergence groups, and the corresponding extension of the Pontryagin duality is the continuous duality. We prove that local quasi-convexity is a necessary condition for a convergence group to be creflexive. Further, we prove that every character group of a convergence group is locally quasi-convex. 2010 MSC: 43A40; 54A20; 54H11.\",\"PeriodicalId\":8046,\"journal\":{\"name\":\"Applied general topology\",\"volume\":\"31 1\",\"pages\":\"193\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied general topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4995/AGT.2021.14585\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied general topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4995/AGT.2021.14585","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Duality of locally quasi-convex convergence groups
In the realm of the convergence spaces, the generalisation of topological groups is the convergence groups, and the corresponding extension of the Pontryagin duality is the continuous duality. We prove that local quasi-convexity is a necessary condition for a convergence group to be creflexive. Further, we prove that every character group of a convergence group is locally quasi-convex. 2010 MSC: 43A40; 54A20; 54H11.
期刊介绍：
The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.
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