Intersection of Closed Sets is Closed

Theorem

Topology

Let $T = \struct {S, \tau}$ be a topological space.

Then the intersection of an arbitrary number of closed sets of $T$ (either finitely or infinitely many) is itself closed.

Normed Vector Space

Let $M = \struct {X, \norm {\, \cdot \,} }$ be a normed vector space.

Then the intersection of an arbitrary number of closed sets of $M$ (either finitely or infinitely many) is itself closed.