Karl Jones: Created page with "In mathematics, a '''topological group''' is a group G together with a topological space on G such that the group's binary operation and the gr..."

2016-10-14T15:42:07Z

Created page with "In mathematics, a '''topological group''' is a group G together with a topological space on G such that the group's binary operation and the gr..."

New page

In [[mathematics]], a '''topological group''' is a [[Group (mathematics)|group]] G together with a [[topological space]] on G such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology.

== Description ==

A topological group is a [[mathematical object]] with both an [[algebraic structure]] and a [[topological structure]].

Thus, one may perform algebraic operations, because of the group structure, and one may talk about continuous functions, because of the topology.

Topological groups, along with [[Continuous group action|continuous group actions]], are used to study continuous symmetries, which have many applications, for example, in [[physics]].

== See also ==

* [[Algebraic group]]
* [[Compact group]]
* [[Continuous group action]]
* [[Lie group]]
* [[Locally compact group]]
* [[Profinite group]]
* [[Topological ring]]
* [[Topological space]]

== External links ==

* [https://en.wikipedia.org/wiki/Topological_group Topological group] @ Wikipedia

[[Category:Mathematics]]
[[Category:Topology]]

Topological group - Revision history

Karl Jones: Created page with "In mathematics, a '''topological group''' is a group G together with a topological space on G such that the group's binary operation and the gr..."