open mapping theorem OpenMappingTheorem 2002-12-07 08:59:53 2006-09-16 12:51:20 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 There are two important theorems having this \PMlinkescapetext{name}. $\bullet$ In the context of functions of a complex variable: \textbf{Theorem.} Every non-constant analytic function on a region is an open mapping. $\bullet$ In the context of functional analysis: \textbf{Theorem.} Every surjective continuous linear mapping between two Banach spaces is an open mapping.