# Urysohn's lemma

From Topospaces

*This article gives the statement, and possibly proof, of a basic fact in topology.*

## Statement

Let be a Normal space (?) (i.e., a topological space that is T1 and where disjoint closed subsets can be separated by disjoint open subsets). Suppose are disjoint closed subsets of . Then, there exists a continuous function such that for all , and for all .

Note that the T1 assumption is not necessary, so Urysohn's lemma also holds for normal-minus-Hausdorff spaces, which is what many point set topologists are referring to when they use the term *normal space*.