Assume thatA,Bare compact, disjoint, nonempty subsets ofM. Prove that there area0Aandb0Bsuch that for allaAandbBwe have d(a0, b0)d(a, b). [The...
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Assume that A,B are compact, disjoint, nonempty subsets of M. Prove that there

are a0 ∈A and b0 ∈B such that for all a∈A and b∈B we have d(a0, b0) ≤ d(a, b).

[The points a0, b0 are closest together.]

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