Banach–Alaoglu Theorem

Banach–Alaoglu Theorem

The closed unit ball in the dual of a normed space is weak* compact.

The Banach–Alaoglu Theorem is a special case of the following result:

Alaoglu–Bourbaki Theorem

The polar of a neighborhood of zero in a locally convex space is weak* compact.

See Alaoglu–Bourbaki Theorem for more information.