Let \(\Omega\subseteq\CC\) be open, let \(K\subseteq\Omega\), and let \(\mathcal F\) be a family of holomorphic functions on \(\Omega\). The family \(\mathcal F\) is equicontinuous on \(K\) if for every \(\varepsilon>0\) there exists \(\delta>0\) such that \[ \abs{f(z)-f(w)}<\varepsilon\qquad\text{for all } f\in\mathcal F \text{ and all } z,w\in K \text{ with } \abs{z-w}<\delta. \]
Equicontinuity on a set
D-PPYCK