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Unformatted text preview: x + f ( x ) and lim x  f ( x ) both exist and are nite. Prove that f is uniformly continuous. Part 3 5. Let K be a compact metric space with metric d and suppose f : K K is distance preserving , meaning that d ( f ( x ) ,f ( y )) = d ( x,y ) for all x,y K . Prove that f ( K ) = K . 6. Problem 1 from page 114. 1...
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This note was uploaded on 02/15/2012 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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