Urysohn's lemma

Statement
Let $$X$$ be a fact about::normal space (i.e., a topological space that is T1 and where disjoint closed subsets can be separated by disjoint open subsets). Suppose $$A,B$$ are disjoint closed subsets of $$X$$. Then, there exists a continuous function $$f:X \to [0,1]$$ such that $$f(a) = 0$$ for all $$a \in A$$, and $$f(b) = 1$$ for all $$b \in B$$.

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.

Related facts

 * Tietze extension theorem
 * Hahn-Dieudonne-Tong insertion theorem