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Nowhere lipshcitz function

  1. Sep 19, 2011 #1
    I need to show, using Baire Category Theorem, that there exits a continuous function
    f: [0,1] to R , that isn't Lipschitz on the interval [r,s] for every 0<=r<s<=1 .

    I defined the set A(r,s) to be all the continuous functions that are lipschitz on the interval [r,s]. I showed that A(r,s) is closed , but i'm having trouble showing it's nowhere dense.

    help please! :)
  2. jcsd
  3. Sep 22, 2011 #2
    Would you you let us know the version of Baire's thm. you are trying? Also, which topology /metric did you use?
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