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: [582]

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[582] **Forster Otto**: “Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen”, Vieweg Studium, 1984