Compact convergence

In mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence that generalizes the idea of uniform convergence. It is associated with the compact-open topology.
Definition.
Let formula_1 be a topological space and formula_2 be a metric space. A sequence of functions
is said to converge compactly as formula_5 to some function formula_6 if, for every compact set formula_7,
uniformly on formula_9 as formula_5. This means that for all compact formula_11,