Topological semigroup
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 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 – topological group whose group is abelianPages 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
- ^ Artur Hideyuki Tomita. On sequentially compact both-sides cancellative semigroups with sequentially continuous addition.
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