Let \(A\subset\mathbb R^n\) be a subset \(A\) of the $n$-dimensional metric space of real numbers $\mathbb R^n$. $A$ is compact if and only if $A$ is closed and bounded.
(This theorem was first proven by Heinrich Eduard Heine and Émile Borel.)
| | | | | created: 2017-03-10 21:01:36 | modified: 2017-03-10 21:08:37 | by: bookofproofs | references: 
 Forster Otto: “Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen”, Vieweg Studium, 1984