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Bypass redirect so I don't have to later.
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 (mathematics)|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 a [[completely regular space]].
Every group G can be turned into a topological group by giving G the [[discrete topology]]. Every topological group is a [[completely regular space]].