BlochsTheorem 2002-12-11 10:03:50 2002-12-11 10:12:46 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 $f$ be an holomorphic function on a region containing the closure of the disk $D=\{z\in\mathbb{C}:|z|<1\}$, such that $f(0)=0$ and $f'(0)=1$. Then there is a disk $S\subset D$ such that $f$ is injective on $S$ and $f(S)$ contains a disk of radius $\frac{1}{72}$.