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Theorem: Theorem of BolzanoWeierstrass
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
Table of Contents
Proofs: 1
Mentioned in:
Theorems: 1
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References
Bibliography
 Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984