# Equicontinuity implies Uniform Equicontinuity

• 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:

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