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Unformatted text preview: X Y with Y a nite set. Use the previous problem to show that (a) X = Y if and only if  X  =  Y  . (b) X Y if and only if  X  <  Y  . (6) Suppose that X and Y are nonempty nite sets of cardinality n . Prove that a map X Y is a surjection if and only if it is an injection. (7) Let X and Y be nite sets (possibly empty). Prove that  X Y  =  X   Y  . (8) Suppose that { 1 ,...,n } X is a surjection. Prove that  X  n . (Hint: Do induction on n .) (9) Let f : X Y be a function between metric spaces ( X,d ), ( Y,f ). Using the denition of continuity from class, prove that f is continuous if and only if the inverse image of every open set is open, i.e. for all open sets U Y , f1 U is an open set in X . 1...
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This note was uploaded on 05/04/2011 for the course MATH 73 taught by Professor Danberwick during the Spring '09 term at University of California, Berkeley.
 Spring '09
 DANBERWICK
 Math, Division

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