Difference between revisions of "Topological group"
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| − | A topological group is a [[topological space]] that is also a group such that the [[binary operation]] defined on the group is a continuous map. | + | A '''topological group''' is a [[topological space]] that is also a [[Group (mathematics)|group]] such that the [[binary operation]] defined on the group is a [[continuous function|continuous map]], as is the operation of inversion. |
| − | Every group G can be turned into a topological group by giving G the [[discrete topology]]. Every topological group is [[completely regular]]. | + | Every group G can be turned into a topological group by giving G the [[discrete topology]]. Every topological group is a [[completely regular space]]. |
| − | [[ | + | [[Category:Topology]] |
| + | [[Category:Algebra]] | ||
Latest revision as of 20:41, July 13, 2016
A topological group is a topological space that is also a group such that the binary operation defined on the group is a continuous map, as is the operation of inversion.
Every group G can be turned into a topological group by giving G the discrete topology. Every topological group is a completely regular space.