Exercise 18, § 10

Let X be the locally compact subspace $[0, +\infty[$ of R. Let S be the equivalence relation on X whose equivalence classes are the sets $\{x, 1/x\}$ for $0 < x \leq 1$ and the set $\{0\}$. Show that S is open, that the graph of S is closed in $X \times X$ and that $X/S$ is compact, but that S is not closed.*