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HomeMIT 18.100B Real Analysis, Spring 2025Lecture 14: Sequential Compactness; Bolzano–Weierstrass Theorem in a Metric Space
Lecture 14: Sequential Compactness; Bolzano–Weierstrass Theorem in a Metric Space
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We show the Bolzano-Weierstrass theorem in a metric space. This theorem states that for a metric space, a sequence contained in a compact subset has a convergent subsequence.