[0RR]Difficulty:*.Let \((X,d)\) be a metric space. Show that \(E⊆ X\) is disconnected if and only if ”there are two disjoint open sets, each of which intersect \(E\) and such that \(E\) is covered by their union” (see the proposition formalized in eqn. [(8.49)] in the exercise [0JK]).
