Question: Let (An) be a nested decreasing sub-sequence of nonempty closed sets in the metric space M (a) If M is complete and diam A_n

Let (An) be a nested decreasing sub-sequence of nonempty closed sets in the metric space M

(a) If M is complete and diam A_n → ∞ as n → ∞, show that ⋂A_n is exactly one point.

(b) To what assertions do the sets [n, ∞) provide counter examples?

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