# Nowhere lipshcitz function

1. Sep 19, 2011

### itzik26

hey,
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.