PerfectSet 2002-12-24 07:31:01 2005-08-04 04:46:30 Definition perfect % 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 set is called \textit{perfect} if it is equal to the set of its limit points. An non-trivial example of a perfect set is the \PMlinkid{middle-thirds Cantor set}{2083}. In fact a more general class of sets is referred to as Cantor sets, which all have (among others) the property of being perfect.