Question: Let {Kn}, n e N, be a decreasing sequence of nonempty compact sets in a metric space (that is, K1 3K2 D , and anQ,

Let {Kn}, n e N, be a decreasing sequence of nonempty

Let {Kn}, n e N, be a decreasing sequence of nonempty compact sets in a metric space (that is, K1 3K2 D , and anQ, V n). a) Prove that 00 n Kn at 0. n=1 b) Give a counterexample that if in the statement \"compact\" is replaced with \"closed\" the result is no longer valid. c) Give a counterexample that if in the statement \"compact\" is replaced with \"bounded\" the result is no longer valid

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