A topological space $X$ is said to be normal if $X$ is $T_1$ (i.e. singletons are closed), and for all disjoint closed sets $D,F\subseteq X$ there exist disjoint open sets $U$ and $V$ such that $C\subseteq U$ and $D\subseteq V$ (i.e, $X$ is also $T_4$ .

Some authors do not require the $T_1$ axiom as part of this definition.