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Unformatted text preview: b n ) is bounded as well. 5)True or False (justify your answer!): a) For any open set A R , we have int ( A ) = A . b) Let V be the space of all functions f : [0 , 1] R , and dene k f k =  f (0)  . Is ( V, k k ) a eld with a norm, if we use the usual sum and multiplication of real valued functions? 6) Show by induction that r 2 + q 2 + 2 + ...  {z } n roots = 2 cos 2 n +1 . Then use this equality to nd the limit of the recursive sequence given by a 1 = 2 a n = 2 + a n n > 1 . 7) Give an example of a countable compact subset of ( R ,d ), where d is the Euclidean metric. 1...
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This note was uploaded on 12/07/2011 for the course MATH 18.100B taught by Professor Prof.katrinwehrheim during the Fall '10 term at MIT.
 Fall '10
 Prof.KatrinWehrheim

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