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Unformatted text preview: MATH 74 QUIZ 2 REVIEW The following are the major topics: (1) Cardinality, Pigeonhole Principle and Finite Sets : Minima and maxima for finite subsets of the real line, countable and uncountable sets. (2) Metric Spaces and Continuity : Open and closed sets, open balls, intersection and unions of open and closed sets, different equivalent notions of continuity, limit points, closure of sets, isometries and homeomorphisms. (3) Sequences : Cauchy sequences, complete metric spaces, limits and continuity, supremum, infimum. (4) Compactness : bounded, totally bounded, open covers, continuous image of compact sets are com pact (statement and proof), HeineBorel Theorem, extreme value theorem. (5) Connectedness : connected subsets of R , continuous image of connected sets are connected (state ment and proof), intermediate value theorem. (6) Contraction Mapping Theorem: statement of the theorem....
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This note was uploaded on 05/04/2011 for the course MATH 73 taught by Professor Danberwick during the Spring '09 term at University of California, Berkeley.
 Spring '09
 DANBERWICK
 Continuity, Division, Sets

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