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In mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence which generalizes the idea of uniform convergence. It is associated with the compact-open topology.
Let (X, \mathcal{T}) be a topological space and (Y,d_{Y}) be a metric space. A sequence of functions
is said to converge compactly as n \to \infty to some function f : X \to Y if, for every compact set K \subseteq X,
converges uniformly on K as n \to \infty. This means that for all compact K \subseteq X,
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