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Completeness and Compactness

Completeness and compactness — the spaces where analysis happens, from contractions to uniform continuity.

1. Metric Spaces — 5. Topology
2. Contraction Mapping Principle — 5. Topology
3. Baire Category Theorem — 5. Topology
4. Baire Class 1 Functions — 5. Topology
5. The Contraction Cobweb — 10. Differentiation
6. Compact Sets — 5. Topology
7. Arzelà–Ascoli Theorem — 6. Approximation
8. A Convergent Subsequence Always Hides Inside — 3. Sequences
9. The Extreme Value Theorem — 4. Continuity
10. Uniform Continuity — 4. Continuity