closed graph theorem ClosedGraphTheorem 2002-12-09 15:00:40 2006-07-27 13:27:44 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 A linear mapping between two Banach spaces $X$ and $Y$ is continuous if and only if its \PMlinkname{graph}{Graph2} is a closed subset of $X\times Y$ (with the product topology).