# Equicontinuity implies Uniform Equicontinuity

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• May 16th 2011, 04:33 PM
orbit
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
• May 17th 2011, 08:01 AM
Tinyboss
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?