A normal space is a topological space $X$ such that whenever $A$ and $B$ are disjoint closed subsets of $X$ then there are disjoint open subsets $U$ and $V$ of $X$ such that $A\subseteq U$ and $B\subseteq V$

(Note that some authors include $\mathrm{T}_1$ in the definition, which is equivalent to requiring the space to be Hausdorff.)

Urysohn's Lemma states that $X$ is normal if and only if whenever $A$ and $B$ are disjoint closed subsets of $X$ then there is a continuous function $f\colon X\to[0,1]$ such that $f(A)\subseteq\{0\}$ and $f(B)\subseteq\{1\}$ (Any such function is called an Urysohn function.)

A corollary of Urysohn's Lemma is that normal <</A>61#>$\mathrm{T}_1$ http://planetmath.org/encyclopedia/T1Space.html spaces are completely regular.