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Question

Let (X, d) be a metric space.

a) Assume that A is a (finite or infinite) collection of open sets. Show that

the union of these open sets is open.

b) Assume that A1, A2, . . . , An is a finite collection of open sets. Show

that the intersection A1 ∩ A2 ∩ . . . ∩ An is open.

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