contractible Contractible 2002-01-23 14:23:02 2007-02-15 22:30:29 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 A topological space is said to be \emph{contractible} if it is homotopy equivalent to a point. Equivalently, the space is contractible if a constant map is homotopic to the identity map. A contractible space has a trivial fundamental group.