Definition (Equicontinuous)

Let $\mathscr{F}$ be a collection of complex-valued functions on a Metric Space $(X,d)$. We say $\mathscr{F}$ is equicontinuous if $$\forall\epsilon>0, \exists\delta>0:d(x,y)<\delta\implies|f(x)-f(y)|<\epsilon,\forall f\in \mathscr{F}$$