Stable4 2008-03-26 19:28:44 2008-03-27 05:50:49 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 subset $S$ of a larger set $T$ is said to a \emph{stable subset} for a function $f: T\to T$ \underline{iff} $f(S)\subset S$.\\ Alternative phrasings with the same meaning are: \begin{itemize} \item $f$ is an invariant subset for $f$ \item $f$ stabilizes $S$ \item $S$ is stable under (the action of) $f$ \item $S$ is invariant under (the action of) $f$ \item $S$ is left stable by/under $f$ \item $S$ is left invariant by/under $f$ \end{itemize}