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Compactness and Tychonoff

Why this is asked: Heine–Borel is ℝⁿ-only. In general spaces use open covers or the finite intersection property; in metric spaces sequential compactness is equivalent.

Compactness in general spaces

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The compactness facts that need Hausdorff, and the ones that do notinteractive

Compact implies closed is false without it — here is the space where it fails.

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Which of the following statements about compact spaces are true?

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Open this in the full syllabus view · Unit 2