Heine-Borel theorem HeineBorelTheorem 2002-01-01 22:37:48 2002-06-11 05:39:22 Theorem \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} A subset $A$ of $\mathbb{R}^n$ is compact if and only if $A$ is \PMlinkname{closed}{TopologicalSpace} and bounded.