Axioms of Continuous Separation

For a $T_1$-space $X$, let $Cld(X)$ denote all its nonempty closed subsets and $T_4(X)=\{(F_1,F_2)\in Cld(X)^2:F_1\cap F_2=\emptyset\}$. In terms of closed sets, $X$ is $T_4$ iff for each $(F_1,F_2)\in T_4(X)$, there is a pair of closed sets $ϕ_1(F_1,F_2)$ and $ϕ_2(F_1,F_2)$ such that their union is