# Math Help - Equicontinuity implies Uniform Equicontinuity

1. ## Equicontinuity implies Uniform Equicontinuity

Let A be a equicontinuous subset of C(X,F). Show that A is Uniform equicontinuous, ie:

$$\forall \varepsilon \succ 0,\exists \delta \succ 0/{\left\| {f(x) - f({x_0})} \right\|_F} \prec \varepsilon ,\forall f \in A,\forall x,{x_0} \in X,d\left( {x,{x_0}} \right) \prec \delta$$

Please help me, I have a test tomorrow.

Regards

Felipe

2. It's not true as stated. For example, let A={f}, where f is not uniformly continuous. Are you sure you didn't leave out any hypotheses?