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

  1. ^ Artur Hideyuki Tomita. On sequentially compact both-sides cancellative semigroups with sequentially continuous addition.


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