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## Theorem: Heine-Borel Theorem

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]

## 1.Proof: (related to "Heine-Borel Theorem")

(none)

### Bibliography (further reading)

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