In mathematics, a topological semigroup is a semigroup that is simultaneously a topological space, and whose semigroup operation is continuous.^[1]

Every topological group is a topological semigroup.

See also

• Analytic semigroup
• Compact group – Topological group with compact topology
• Complete field – algebraic structure that is complete relative to a metricPages displaying wikidata descriptions as a fallback
• Ellis–Numakura lemma – A compact topological semigroup with a semicontinuous product has an idempotent element
• Locally compact group – topological group G for which the underlying topology is locally compact and Hausdorff, so that the Haar measure can be definedPages displaying wikidata descriptions as a fallback
• Locally compact quantum group – relatively new C*-algebraic approach toward quantum groupsPages displaying wikidata descriptions as a fallback
• Ordered topological vector space
• Strongly continuous semigroup – Generalization of the exponential functionPages displaying short descriptions of redirect targets
• Topological abelian group – concept in mathematicsPages displaying wikidata descriptions as a fallback
• Topological field – Algebraic structure with addition, multiplication, and divisionPages displaying short descriptions of redirect targets
• Topological group – Group that is a topological space with continuous group action
• Topological module
• Topological ring – ring where ring operations are continuousPages displaying wikidata descriptions as a fallback
• Topological vector lattice
• Topological vector space – Vector space with a notion of nearness

References