BoundedSet 2006-06-11 15:26:09 2006-06-11 15:26:09 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 set in a topological vector space is {\it bounded } if it is absorbed by every neighborhood of 0. That is, $B$ is bounded if for every neighborhood $U$ of 0, there is a $\delta > 0$ such that $\epsilon B \subset U$ for $0 \leq \epsilon < \delta$.