Definition:Cauchy Sequence in Topological Group

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 for every neighborhood $U$ of $e$ there exists $N \in \N$ such that for all $m, n \ge N : a_n a_m^{-1} \in U$.

Also see

 * Definition:Cauchy Sequence in Metric Space