\begin{definition}[Definition:Compact Convergence]
Let $X$ be a topological space.
Let $M$ be a metric space.
Let $\left\langle{f_n}\right\rangle$ be a sequence of mappings $f_n : X \to M$.
Let $f: X \to M$ be a mapping.
Then $f_n$ '''converges compactly''' to $f$ {{iff}} $f_n$ converges uniformly to $f$ on every compact subset of $X$.
\end{definition}