Hello there. I am supposed to show whether or not the function

0,1) \rightarrow \mathbb{R} " alt=" f0,1) \rightarrow \mathbb{R} " /> given by

is uniformly continuous.

I suspect it is not so I'm trying to prove the statement:

such that such that and .

i.e. our choice of delta in the definition of continuity does not depend on a. Any help with this would be appreciated.