Define the distance between two nonempty subsets A and B of R" by

a) Prove that if A and B are compact sets which satisfy A ˆ© B = θ, then dist(A, B) > 0.
b) Show that there exist nonempty, closed sets A, B in R2 such that A ˆ© B = θ but dist(A, B) = 0.

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dist( A, B ) := inflǐx-yll : x ε A and y e B }.