Hahn-Banach theorem (geometric form) HahnBanachgeometricFormTheorem 2005-05-10 13:10:23 2006-10-12 19:19:13 Theorem % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here Let $E$ be a locally convex space $A,B\subset E$, two convex, nonempty and disjoint sets. Suppose that $A$ is closed and $B$ is compact. Then there is a hyperplane which strictly separates $A$ and $B$.