Locally uniform convergence

Let \(\Omega\subseteq\CC\) be open and let \(f_n,f\colon\Omega\to\CC\) for \(n\ge1\). The sequence \((f_n)\) converges locally uniformly to \(f\) on \(\Omega\) if \(f_n\to f\) uniformly on every compact subset \(K\subseteq\Omega\).