Proposition 10

If $X$ is a Hausdorff space, and if $X$ has a continuous section $s$ with respect to the equivalence relation $R$, then $X/R$ is Hausdorff and $s(X/R)$ is closed in $X$.

For ($§ 3$, no. 5) $X/R$ is homeomorphic to the subspace $s(X/R)$ of $X$, which is Hausdorff. Furthermore $s(X/R)$ is the set of all $x \in X$ such that $s(\varphi(x)) = x$, where $\varphi : X \to X/R$ is the canonical mapping; hence the second assertion follows from no. 1, Proposition 2.