Viewing topic: Completely Regular

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Completely Regular

  • Definition: A space X is completely regular if one-point sets are closed in X and if for each point x_0 and each closed set A not containing x_0, there is a continuous function f: X -> [0, 1] such that f(x_0) = 1 an f(A) = {0}.

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

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