The compact-open topology on a space of functions is generated by uniform control on compact subsets. For scalar-valued functions, its basic seminorms are as ranges over compact subsets of the domain.

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  1. Locally uniform convergence
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Compact-open topology by Wikipedia Bot 1
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The compact-open topology is a topology defined on the space of continuous functions between topological spaces, particularly when considering the set of continuous functions from one topological space to another. This topology is especially useful in areas like functional analysis and algebraic topology.
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