Question: We call set ACR closed if every sequence in A converges in A. Let 1 212 213 2... be a sequence of nonempty closed

We call set ACR closed if every sequence in A converges in

We call set ACR closed if every sequence in A converges in A. Let 1 212 213 2... be a sequence of nonempty closed nested subsets of R. (a) If I is a bounded set, prove that n=1 In # 0. [Hint: Use the Bolzano-Weierstrass Theorem] (b) Give a counterexample to show that if I is not assumed to be bounded, then the conclusion in (a) need not be true.

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