Exercise 5, § 3

Let $G$ be a topological group and let $K$ be a normal subgroup of $G$. Considering $G/K$ as a subset of $\mathfrak{B}(G)$, show that the right uniformity on the topological group $G/K$ is induced by the uniformity on $\mathfrak{B}(G)$ constructed from the right uniformity on $G$ by the procedure of Exercise 5 of Chapter II, § 1.