# Heine-Borel theorem

A subset $A$ of $\mathbb{R}^{n}$ is compact if and only if $A$ is closed (http://planetmath.org/TopologicalSpace) and bounded.

Title Heine-Borel theorem HeineBorelTheorem 2013-03-22 12:05:09 2013-03-22 12:05:09 Evandar (27) Evandar (27) 8 Evandar (27) Theorem msc 54D30 Compact ProofOfLeastAndReatestValueOfFunction