Property 2002-09-30 19:23:08 2002-11-17 15:39:52 Definition satisfies as a Chu space % 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 %\PMlinkescapeword{theory} A \emph{property} of a Chu space over $\Sigma$ with carrier $\mathcal{A}$ is some $Y\subseteq \Sigma^\mathcal{A}$. We say that a Chu space $\mathcal{C}=(\mathcal{A},r,\mathcal{X})$ \emph{satisfies} $Y$ if $X\subseteq Y$. For example, every Chu space satisfies the property $\Sigma^\mathcal{A}$.