Viewing topic: Topology Of Compact Convergence

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Topology Of Compact Convergence

  • Definition: Let (Y, d) be a metric space; let X be a topological space. Given an element f of Y^X, a compact subspace C of X, and a number epsilon greater than 0, let B_C(f, epsilon) denote the set of all elements g of Y^X for which sup{d(f(x), g(x))|x in C} is less than epsilon. The sets B_C(f, epsilon) form a basis for a topology on Y^X. It is called the topology of compact convergence (or sometimes the "topology of uniform convergence on compact sets").

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

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