Let K and L be nonempty compact sets, and define d = inf{|r - y|:1€ K and y E L} This turns out to be a reasonable definition for the distance between K and L. (a) If K and L are disjoint, show d > 0 and that d = |r0 – y0| for some ro € K and yo E L. (b) Show that it's possible to have d = 0 if we assume only that the disjoint sets K and L are closed.

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