ContinuousProperMap 2003-04-16 00:28:56 2003-04-16 00:28:56 Definition % 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 \def\sse{\subseteq} \def\bigtimes{\mathop{\mbox{\Huge $\times$}}} \def\impl{\Rightarrow} Let $X, Y$ be topological spaces and $p\colon X\to Y$ a continuous map. The map $p$ is called \emph{continuous proper} if for every compact $K\sse Y$ the preimage $p^{-1}(K)$ is compact in $X$.