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 B , then dist(A, B) 0 b) Show that there exist nonempty, closed sets A, B in R2 such that A B but dist(A, B) 0 dist( A, B ) inflx yll x A and y e B

Question: 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

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 = Î¸, then dist(A, B) > 0.
b) Show that there exist nonempty, closed sets A, B in R2 such that A ˆ© B = Î¸ but dist(A, B) = 0.

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

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a Since both sets are nonempty and x y is bounded below by 0 the dist AB exists and is finite By ... View full answer

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