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    Power Series - Boundedness

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    (a) Suppose E and F are nonempty closed bounded subsets of C. Show that there exist z_0 E E and w_0 E F such that

    | z_0 - w_0 | = inf {| z - w | ; z E E, w E F}.

    (b) Show that this is not true if the boundedness condition on E and F is dropped.

    (c) What if only one of E or F is bounded (but both are still closed)?

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