 | This article relies largely or entirely on a
single source. (May 2024) |
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 metric
- 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 defined
- Locally compact quantum group – relatively new C*-algebraic approach toward quantum groups
- Ordered topological vector space
- Strongly continuous semigroup – Generalization of the exponential function
- Topological abelian group – concept in mathematics
- Topological field – Algebraic structure with addition, multiplication, and division
- Topological group – Group that is a topological space with continuous group action
- Topological module
- Topological ring – ring where ring operations are continuous
- Topological vector lattice
- Topological vector space – Vector space with a notion of nearness
References
 | This algebra-related article is a stub. You can help Wikipedia by expanding it. |
 | This topology-related article is a stub. You can help Wikipedia by expanding it. |
| This article relies largely or entirely on a
single source. (May 2024) |
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 metric
- 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 defined
- Locally compact quantum group – relatively new C*-algebraic approach toward quantum groups
- Ordered topological vector space
- Strongly continuous semigroup – Generalization of the exponential function
- Topological abelian group – concept in mathematics
- Topological field – Algebraic structure with addition, multiplication, and division
- Topological group – Group that is a topological space with continuous group action
- Topological module
- Topological ring – ring where ring operations are continuous
- Topological vector lattice
- Topological vector space – Vector space with a notion of nearness
References
|
| This algebra-related article is a stub. You can help Wikipedia by expanding it. |
|
| This topology-related article is a stub. You can help Wikipedia by expanding it. |