In a normal topological space, any two disjoint closed sets can be separated by a continuous real-valued function taking the value zero on one set and one on the other. Proved by Pavel Urysohn, it is a foundational tool for constructing continuous functions in general topology.
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StatementA topological space is normal if and only if any two disjoint closed subsets of it can be separated by a continuous function into the unit interval, taking the value 0 on one subset and 1 on the other. 1 Classification
Statement FormCharacterization Theorem 1 Urysohn's Lemma
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1. Urysohn's Lemma (Wikipedia)
Wikimedia Foundationlead paragraph, theorem statement sentence
In topology, Urysohn's lemma is a lemma that states that a topological space is normal if and only if any two disjoint closed subsets can be separated by a continuous function.
Proved By: Pavel Urysohn, Lead paragraph
In topology, Urysohn's lemma is a lemma that states that a topological space is normal if and only if any two disjoint closed subsets can be
In Group: General Topology, Lead paragraph
In topology, Urysohn's lemma is a lemma that states that a topological space is normal if and only if any two disjoint closed subsets can be separated by a continuous function.
View the Source Pavel Urysohn (Wikipedia)
Principal Result Of: Pavel Urysohn, Article textQuote, Principal Result Of: Pavel Urysohn, Article text
Pavel Samuilovich Urysohn (in Russian: Па́вел Самуи́лович Урысо́н; 3 February 1898-17 August 1924) was a Soviet mathematician who is best known for his contributions to the theory of topological dimension, and for developing Urysohn's metrization theorem and Urysohn's lemma, both of which are fundamental results in
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