---
title: Banach–Alaoglu Theorem
parent: Functional Analysis Basics
nav_order: 3
# cspell:words
---

# {{ page.title }}

{: .theorem-title }
> {{ page.title }}
> {: #{{ page.title | slugify }} }
>
> The closed unit ball in the dual of a normed space is weak\* compact.

{% proof %}
{% endproof %}

## Generalization: Alaoglu–Bourbaki