HeineCantorTheorem 2002-06-07 09:32:28 2003-03-17 18:31:16 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 $X,Y$ be uniform spaces, and $f: X \rightarrow Y$ a continuous function. If $X$ is compact, then $f$ is uniformly continuous. For instance, if $f: [a,b] \rightarrow \mathbb{R}$ is a continuous function, then it is uniformly continuous.