Urysohn lemma
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The Urysohn lemma states:
If A, B are two disjoint, closed subsets of a normal space X, then there exist a continuous function f : X → [0, 1], such that f(A) = 0 and f(B) = 1.
The converse of the Urysohn lemma also holds: if there is such a continuous function for any two disjoint closed sets A and B in X, then X is normal.