Pseudocompact and precompact subsemigroups of topological groups
Julio C\'esar Hern\'andez Arzusa

TL;DR
This paper explores conditions under which subsemigroups of topological groups are actually subgroups, focusing on properties like pseudocompactness and precompactness, and establishing new criteria for these structures.
Contribution
It introduces new sufficient conditions for subsemigroups to be subgroups, specifically relating to pseudocompactness and precompactness in topological groups.
Findings
Closed precompact subsemigroups are subgroups.
Open pseudocompact monoids are subgroups.
Provides criteria extending previous compactness conditions.
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 \cite{Kosh, 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Fuzzy and Soft Set Theory · Rings, Modules, and Algebras
