Normal topological space/Definition

Definition

A topological space, $(X,\mathcal{ J })$, is said to be normal if:

• $\forall E,F\in C(\mathcal{J})\ \exists U,V\in\mathcal{J}[E\cap F=\emptyset\implies(U\cap V=\emptyset\wedge E\subseteq U\wedge F\subseteq V)]$ - (here $C(\mathcal{J})$ denotes the collection of closed sets of the topology, $\mathcal{J}$)