Suppose A and B are subsets of R, and define:
d(A,B) = inf{|a−b| : a ∈ A,b ∈ B}.
(a) Show that if A∩B 6= ∅, then d(A,B) = 0.
(b) If A is compact, B is closed, and A∩B = ∅, show d(A,B) >
0.
(c) Find 2 closed, disjoint subsets of R (say A and B) with
d(A,B) = 0