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 function|continuous map]]. | A topological group is a [[topological space]] that is also a group such that the [[binary operation]] defined on the group is a [[continuous function|continuous map]]. | ||
| − | 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: mathematics]] | [[category: mathematics]] | ||
Revision as of 22:21, March 22, 2007
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.
Every group G can be turned into a topological group by giving G the discrete topology. Every topological group is a completely regular space.