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Quiz 02 Review Sheet

Quiz 02 Review Sheet - MATH 74 QUIZ 2 REVIEW The following...

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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), Heine-Borel 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. Note that Hausdorff distance will not be on the quiz. Sample questions : (1) Define . . . (anything above).
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