Unformatted text preview: x → + ∞ f ( x ) and lim x →-∞ f ( x ) both exist and are ﬁnite. 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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- Fall '10
- Topology, Metric space, compact metric space