Regular topological space/Definition

Definition

A topological space, $(X,\mathcal{ J })$ is regular if:

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

Warning:Note that it is $E\subset U$ not $\subseteq$, the author () like me is pedantic about this, so it must matter