Exercise 2, § 5

Let $G$ be a locally compact group, $\mathfrak{F}(G)$ the uniform space of closed subsets of $G$ (defined in No. 6 or in Exer. 1). Prove directly that the set $\Sigma$ of closed subgroups of $G$ is closed in $\mathfrak{F}(G)$ (without using Prop. 3 of No. 1).