Axioms of Continuous Separation

Zhongqiang Yang, Nada Wu

For a $T_1$-space $X$, let $Cld(X)$ denote all its nonempty closed subsets and $T_4(X)=\{(F_1,F_2)\in Cld(X{)}^2:F_1\cap F_2=\varnothing \}$. In terms of closed sets, $X$ is $T_4$ iff f…