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

$\displaystyle f0,1) \rightarrow \mathbb{R} $ given by $\displaystyle f(x) = \frac{1}{x^2} $

is uniformly continuous.

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

$\displaystyle \exists \epsilon > 0 $ such that $\displaystyle \forall \delta > 0 \exists x,a \in (0,1) $ such that $\displaystyle |x-a| < \delta $and $\displaystyle | \frac{1}{x^2} - \frac{1}{a^2} | < \epsilon $.

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