Definition:Compact Convergence

Definition

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 $f$ if and only if $f_n$ converges uniformly to $f$ on every compact subset of $X$.