Urysohn lemma

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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 xX, and ƒ (A) = 0 and ƒ (B) = 1.
References in periodicals archive ?
In 2016, by using Urysohn's lemma and Schauder-Tychonoff fixed point theorem, D.
Indeed, if y is a point outside this (weakly) closed set, then by Urysohn's lemma, there is f [member of] C([OMEGA]*) such that f [greater than or equal to] 0, f (y)=1 and f ([x.sup.n.sub.i]) = 0 for all n and i=1, ...
Pavel Uryson (February 3, 1898, Odessa--August 17, 1924, Batz-sur-Mer) was a Jewish mathematician who is best known for his contributions in the theory of dimension, and for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology.