\begin{definition}[Definition:Locally Uniform Convergence/General Definition]
Let $\struct {X, \tau}$ be a topological space.
Let $\struct {M, d}$ be a metric space.
Let $\sequence {f_n}$ be a sequence of mappings $f_n: X \to M$.
Then $f_n$ '''converges locally uniformly''' to $f: X \to M$ {{iff}} every point of $X$ has a neighborhood on which $f_n$ converges uniformly to $f$.
\end{definition}