Let (X, d) be a metric space. a) Assume that A is a (finite or infinite) collection of open sets. Show thatthe union of these open sets is open.b) Assume that A1, A2, . . . , An is a finite collection of open sets. Showthat the intersection A1 ∩ A2 ∩ . . . ∩ An is open.

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.