508F06Ex1s(1)

# 508F06Ex1s(1) - Exam 1 Math 508 Jerry L Kazdan 12:00 1:20...

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Math 508 Exam 1 Jerry L. Kazdan October 12, 2006 12:00 – 1:20 Directions This exam has three parts, Part A has 4 problems asking for Examples (20 points, 5 points each), Part B asks you to describe some sets (20 points), Part C has 4 traditional problems (60 points, 15 points each). Closed book, no calculators – but you may use one 3 00 × 5 00 card with notes. Part A: Examples (4 problems, 5 points each). Give an example of an inFnite set in a metric space (perhaps R ) with the speciFed property. A–1. Bounded with exactly two limit points. A–2. Containing all of its limit points. A–3. Distinct points { x j } , j = 1 , 2 , . . . with x i 6 = x j for i 6 = j that is compact. A–4. Closed and bounded but not compact. Part B: Classify sets (20 points) ±or each of the following sets, circle the listed properties it has: a) { 1 + 1 n R , n = 1 , 2 , 3 , . . . } open closed bounded compact countable b) { 1 } ∪ { 1 + 1 n R , n = 1 , 2 , 3 , . . . } open closed bounded

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508F06Ex1s(1) - Exam 1 Math 508 Jerry L Kazdan 12:00 1:20...

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