Corollary 2

Let G be a topological group and let H be a discrete subgroup of G. Let H operate on G by right translations. Then the canonical mapping of G into the space $G/H$ of left classes modulo H endows G with a structure of principal covering of $G/H$ of group H.

Let V be a neighbourhood of the identity element $e$ of G such that $H\cap V =\{e\}$. There exists an open neighbourhood U of $e$ in G such that $U^{-1}\cdot U\subset V$ (TG, III, p. 3) and consequently $U\cap U\cdot h=\emptyset$ for every $h\in H,h=\not e$. Corollary 2 of I, p. 100 therefore follows from theorem 1.