Urysohn lemma

Urysohn lemma

[′u̇r·ē‚zōn ‚lem·ə]

(mathematics)

If A and B are disjoint, closed sets in a normal space X, there is a real-valued function ƒ such that 0 ≤ ƒ(x) ≤ 1 for all x ∈ X, and ƒ (A) = 0 and ƒ (B) = 1.