quasi-compact QuasiCompact 2002-02-02 03:46:52 2006-07-29 15:44:27 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 called {\em quasi-compact} if every open cover of it has a finite subcover. The distinction \PMlinkescapetext{between} compact spaces and quasi-compact spaces exists because some people insist that a space that is compact must be a Hausdorff space. This distinction occurs for example in Robin Hartshorne's book {\sl Algebraic Geometry\/}.