Let \(X\) be a topological space, let \(x\in X\), and let \(\mathcal F\subseteq C(X)\) be a family of continuous functions \(X\to\CC\). The family \(\mathcal F\) is equicontinuous at \(x\) if \[ \forall \varepsilon > 0 \quad \exists \text{ an open set } U \ni x \quad \forall y\in U \quad \forall f\in \mathcal{F}: \quad \abs{f(y) - f(x)} < \varepsilon. \]
Equicontinuity at a point
D-2CCDB