Pseudocompact and precompact subsemigroups of topological groups

2020/12/19 by Julio César Hernández Arzusa, Arzusa, Julio César Hernández
Decision Sciences · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2012.10570

openalex publication_date 2020/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give sufficient conditions under which a subsemigroup of a topological group is a subgroup, adding to the results given in \citeKosh, can, axioms, forum, Hof, cc, locally where conditions exist (such as locally compactness, compactness, feeble compactness and sequential compactness) for a semigroup to be a group. In our work we proved that closed precompact subsemigroups of topological groups are semigroups, just like open pseudocompact monoids of topological groups.

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