mat314w08review2

mat314w08review2 - The characterization of compact in terms...

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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 denitions 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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This note was uploaded on 03/11/2008 for the course MATH 314 taught by Professor Givens during the Winter '08 term at Cal Poly Pomona.

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mat314w08review2 - The characterization of compact in terms...

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