Let A and B be nonempty subsets of a metric space (X, d ). We define the distance from A to B by (a) Give an example to show that it is possible for two disjoint closed sets A and B to satisfy d (A,...

Let A and B be nonempty subsets of a metric space (X, d ). We define the distance from A to B by

(a) Give an example to show that it is possible for two disjoint closed sets A and B to satisfy d (A, B) = 0.

(b) Prove that if A is closed and B is compact and A ∩ B = ∅, then d (A, B) > 0