Exercise 12, § 3

Let $X$ be the subspace $[0, 1]$ of the real line $\mathbf{R}$, and let $S$ be the equivalence relation on $X$ whose equivalence classes are $\{0, 1\}$ and the sets $\{x\}$ for $0 < x < 1$. Show that $X$ has no continuous section with respect to $S$. \*