Suppose A and B are subsets of R, and deﬁne: d(A,B) = inf{|a−b| : a ∈...

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

Expert Solution

Colby Messinger answered 9 months ago

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