Exercise 16, § 10

Let X be a locally compact space, R an equivalence relation on X, C the graph of R in $X \times X$. Show that C is closed in $X \times X$ if and only if, for each compact subset K of X, the saturation of K with respect to R is closed in X. (To prove necessity, use Corollary 5 of Theorem 1 of no. 2).