# uniformly equicontinuous

A family $\mathcal{F}$ of functions from a metric space $(X,d)$ to a metric space $(X^{\prime},d^{\prime})$ is uniformly equicontinuous if, for each $\varepsilon>0$ there exists $\delta>0$ such that,

 $\forall f\in\mathcal{F},\;\forall x,y\in X,\;\;d(x,y)<\delta\Rightarrow d^{% \prime}(f(x),f(y))<\varepsilon.$
Title uniformly equicontinuous UniformlyEquicontinuous 2013-03-22 13:14:33 2013-03-22 13:14:33 Koro (127) Koro (127) 6 Koro (127) Definition msc 54E50 Equicontinuous