Uniform limit theorem

Let \(X\) be a topological space, and let \(f_n\colon X\to\CC\) for \(n\geq1\) and \(f\colon X\to\CC\) be functions. If each \(f_n\) is continuous and \(f_n\to f\) uniformly on \(X\), then \(f\) is continuous.