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+---
+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