{"title":"近端群紧致性的研究","authors":"Surabhi Tiwari","doi":"10.1007/s13370-025-01341-6","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we revisit the concept of proximal groups, which are generalization of topological groups. Further, we prove Kuratowski–Mrówka theorem for proximity spaces which motivate us to define categorically compact proximal groups. Finally, we prove Tychonoff theorems for proximal groups. The study is supported by various examples.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A study of compactness for proximal groups\",\"authors\":\"Surabhi Tiwari\",\"doi\":\"10.1007/s13370-025-01341-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we revisit the concept of proximal groups, which are generalization of topological groups. Further, we prove Kuratowski–Mrówka theorem for proximity spaces which motivate us to define categorically compact proximal groups. Finally, we prove Tychonoff theorems for proximal groups. The study is supported by various examples.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"36 3\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-06-25\",\"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/s13370-025-01341-6\",\"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/s13370-025-01341-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we revisit the concept of proximal groups, which are generalization of topological groups. Further, we prove Kuratowski–Mrówka theorem for proximity spaces which motivate us to define categorically compact proximal groups. Finally, we prove Tychonoff theorems for proximal groups. The study is supported by various examples.
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