**Unformatted text preview: **3. The Contraction Mapping Theorem 2.7.16. 4. Every closed subset of a compact metric space is compact (Theorem 2.8.14) 5. Two vector spaces X and Y over the same Feld are isomorphic if and only if dim X = dim Y (Theorem 3.3.3). 6. Mean Value Theorem (Theorem 4.1.7). You may use either the proof given in class (which did not depend on Rolle’s Theorem) or you may prove the Mean Value Theorem, assuming Rolle’s Theorem. 1...

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- Fall '08
- Staff
- Topology, Mean Value Theorem, Metric space, List of Theorems