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508F08Ex2s(1) - Exam 2 Math 508 December 4 2008 Jerry L...

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Math 508 Exam 2 Jerry L. Kazdan December 4, 2008 10:30 – 11:50 Directions This exam has two parts, Part A has 10 True-False problems (30 points, 3 points each). Part B has 5 traditional problems (70 points, 14 points each). Closed book, no calculators or computers– but you may use one 3 00 × 5 00 card with notes on both sides. Part A: True/False (answer only, no reasons). 10 problems, 3 points each). Circle T or F in in each problem. 1. T F A bounded sequence { a n } of real numbers always has a convergent subsequence. 2. T F A series n =1 a n of complex numbers converges if and only if the corresponding sequence of partial sums is bounded. 3. T F A closed and bounded subset of a complete metric space must be compact. 4. T F If A and B are compact subsets of a metric space, then A B is also compact. 5. T F If M is any metric space and f : M R is any continuous real-valued function, then the function g : M R defined by g ( x ) := ( f ( x )) 2 is always continuous.
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