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...

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.