## Normal Spaces

I'm proving equivalent statements for normal, and I'm stuck at this one. Any help getting started would be appreciated.

We are given that $(X,\Omega)$ is a $T_1$ space and that:

If $H$ and $K$ are disjoint members of $\kappa (\Omega)$, then there exist $U \in \Omega$ such that $H\subseteq U$ and $\bar{U}\cap K = \emptyset$.

I need to prove that:

Each pair of disjoint members of $\kappa (\Omega)$ have disjoint neighborhoods.