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
Canonical name	UniformlyEquicontinuous
Date of creation	2013-03-22 13:14:33
Last modified on	2013-03-22 13:14:33
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	6
Author	Koro (127)
Entry type	Definition
Classification	msc 54E50
Related topic	Equicontinuous