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Definitions in a metric space (X,d): interior point, open set, limit point, closed set, open cover, finite subcover, compact set. Theorems: Heine-Borel Theorem, continuity in terms of preimages of open sets, image of a compact set is compact (Extreme Value Theorem). Examples: interior, closure, open sets, closed sets, compact sets. Proofs: 1 ...
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