Quotient of a topological group by a discrete subgroup

If $\Gamma$ is a discrete subgroup of a topological group $G$, then left translation by $\Gamma$ is a covering-space action. Choose an identity neighbourhood $U$ with $U{U}^{-1}\cap \Gamma =\{1\}$; the translates $\gamma U$ are pairwise disjoint, and the quotient map $G\to \Gamma \backslash G$ restricts to a homeomorphism on each translate.