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## Theorem: Theorem of Bolzano-Weierstrass

Let $X$ be a metric space and let $$A\subset X$$ be a compact subset. Let $(x_n)_{n\in\mathbb N}$ be a sequence of points $$x_n\in A$$. Then $(x_n)_{n\in\mathbb N}$ contains a subsequence $(x_{n_k})_{k\in\mathbb N}$, which converges against some point $$a\in A$$.

### Notes

| | | | | created: 2017-03-12 14:54:41 | modified: 2017-03-12 14:55:15 | by: bookofproofs | references: [582]

## 1.Proof: (related to "Theorem of Bolzano-Weierstrass")

### This work is a derivative of:

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