Viewing topic: Urysohn Lemma

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Urysohn Lemma

  • Definition: Let X be a normal space; let A and B be disjoint closed subsets of X. Let [a, b] be a closed interval in the real line. Then there exists a continuous map f: X -> [a, b] such that f(x) = a for every x in A, and f(x) = b for every x in B.

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

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