204ListofTheorems2006 - 3. The Contraction Mapping Theorem...

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Econ 204–Fall 2006 List of Theorems for the Final Exam You are responsible for the statements of all theorems stated in the text or in class. Understanding the proofs of theorems may help you to answer some questions, so you are advised to try to understand the key ideas behind proofs. In addition, you will be asked to state and prove one of the following theorems: 1. The supremum property (Theorem 1.6.8) 2. Uniqueness of limits of sequences in metric spaces (Theorem 2.2.3).
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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 Rolles Theorem) or you may prove the Mean Value Theorem, assuming Rolles Theorem. 1...
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