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 compactopen topology.
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Let be a topological space and (X_{2},d_{2}) be a metric space. A sequence of functions
is said to converge compactly as to some function if, for every compact set ,
converges uniformly on K as . This means that for all compact ,
