Viewing topic: Compact Open Topology

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Compact Open Topology

  • Definition: Let X and Y be topological spaces. If C is a compact subspace of X and U is an open subset of Y, define S(C, U) = {f|f in G(X, Y) and f(C) is a subset of U}. The sets S(C, U) form a subbasis for a topology on G(X, Y) that is called the compact-open topology.

    Source: Topology (second edition) by James R. Munkres

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