{{one source |date=May 2024}} In mathematics, a '''topological semigroup''' is a semigroup that is simultaneously a topological space, and whose semigroup operation is continuous.<ref>Artur Hideyuki Tomita. [http://tatra.mat.savba.sk/Full/14/10tomita.ps On sequentially compact both-sides cancellative semigroups with sequentially continuous addition.]</ref>
Every topological group is a topological semigroup.<!--TODO: ''Cite a more topical source instead.''-->
==See also== {{div col}} * {{annotated link|Analytic semigroup}} * {{annotated link|Compact group}} * {{annotated link|Complete field}} * {{annotated link|Ellis–Numakura lemma}} * {{annotated link|Locally compact group}} * {{annotated link|Locally compact quantum group}} * {{annotated link|Ordered topological vector space}} * {{annotated link|Strongly continuous semigroup}} * {{annotated link|Topological abelian group}} * {{annotated link|Topological field}} * {{annotated link|Topological group}} * {{annotated link|Topological module}} * {{annotated link|Topological ring}} * {{annotated link|Topological vector lattice}} * {{annotated link|Topological vector space}} {{div col end}}
==References== {{reflist}}
Category:Topological algebra Category:Topological groups
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