mat314w08review2 - Mat 314 Review for Exam 2 The second...

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Mat 314 Review for Exam 2 February 28, 2008 The second exam will be on Thursday, March 6. The exam will cover chapters 3 and 4. In chapter 3, we covered sections 3.1-3.3. In chapter 4, we covered 4.1-4.4. You definitely should know the definitions of the following terms: open set limit point isolated point closed set closure of a set compact set bounded set open cover finite subcover The Cantor set lim x c f ( x ) = L continuous at a point c continuous on a set A bounded function on a set B Also know the following theorems: The union of open sets is open and the finite intersection of open sets is open The Density of Q in R (Theorem 3.2.10) The closure of A is closed (Theorem 3.2.12) Complements of open sets are closed and complements of closed sets are open Heine-Borel Theorem
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Unformatted text preview: • The characterization of compact in terms of open covers (Theorem 3.3.8) • The Sequential Criterion for Functional Limits • Algebraic Limit Theorem for Functional Limits • The Divergence Criterion for Functional Limits • Characterizations of Continuity (Theorem 4.3.2) • The Discontinuity Criterion • Algebraic Continuity Theorem • Composition of Continuous Functions • Preservation of Compact Sets • Extreme Value Theorem The exam may have: • One question that asks you for definitions or statements of theorems. • One question that is very similar to homework problems • One question that asks you for examples • One question that asks you to prove something about functional limits • Other questions...
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  • Winter '08
  • Givens
  • Topology, Metric space, Compact space, General topology, Algebraic Limit Theorem, functional limits

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