Question: Suppose that K is compact in Rn and that for every x K there is an r = r(x) > 0 such that Br(x)

Suppose that K is compact in Rn and that for every x ∈ K there is an r = r(x) > 0 such that Br(x) ∩ K = {x}. Prove that K is a finite set.

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