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<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>

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A study of compactness for proximal groups

  • 期刊论文

  • 发表日期：

    2025年6月25日

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  • Surabhi Tiwari

摘要

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.