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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! :)

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# Lipschitz function and Baire Category Theorem

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