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Definition corrected.
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]].
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 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]].