OpenMapping 2002-12-07 09:14:43 2002-12-07 09:14:43 Definition closed function closed mapping % 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 $X$ and $Y$ be two topological spaces. A function $f:X\rightarrow Y$ is said to be open if $f(U)$ is open for each open subset $U$ of $X$. Accordingly, if $f(C)$ is closed for each closed subset $C$ of $X$, we say that $f$ is closed.