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Unformatted text preview: Part 2 3. For each of the following subsets of R , determine whether the set is open, whether it is closed, and whether it is compact. Also, nd the interior, the limit points and the closure. For this problem you do not need to provide any proofs. (a) { 1 , 2 , 3 } . (b) [1 , 0) (0 , 1]. (c) Q . (d) The complement of Q . Do the same thing for the following subsets of R 2 . (e) { ( x,y ) R 2 : y > } . 1 (f) { ( x,y ) R 2 : x [1 , 0) (0 , 1] } . 4. Problem 13 from page 44. Part 3 5. Let K be a compact metric space, and > 0. Show that there exists N N such that every set of N distinct points in K includes at least two points with distance less than between them. 6. Let K be a compact metric space. Show that K has a subset which is dense and at most countable. 2...
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 Fall '10
 Prof.KatrinWehrheim

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