does bus Exercise 3.3.5. Decide whether the following propositions are true or false. If the claim is valid, supply a short proof, and if the claim is false, provide a counterexample. (a) The arbitrary intersection of compact sets is compact. (b) The arbitrary union of compact sets is compact. (c) Let A be arbitrary, and let K be compact. Then, the intersection Ank is compact. (d) If F1 2 F22 F3 2 F4 2. is a nested sequence of nonempty closed sets, then the intersection 1 Fn +0.

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