# Banach-Alaoglu theorem

Let $X$ be a normed space, and let $X^{*}$ be its dual. Then the closed unit ball of $X^{*}$,

 $\{f\in X^{*}:\|f\|\leq 1\}$

is compact in the weak-$*$ topology.

Title Banach-Alaoglu theorem BanachAlaogluTheorem 2013-03-22 14:48:44 2013-03-22 14:48:44 Koro (127) Koro (127) 6 Koro (127) Theorem msc 46B10 Alaoglu’s theorem