Definition:Cauchy Sequence in Topological Group
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Definition
Let $G$ be a topological group with identity element $e$.
Let $\sequence {a_n}$ be a sequence in $G$.
Then $\sequence {a_n}$ is a Cauchy sequence if and only if for every neighborhood $U$ of $e$ there exists $N \in \N$ such that for all $m, n \ge N : a_n a_m^{-1} \in U$.