# Normal Spaces

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 $\bar{U}\cap K = \emptyset$.
Each pair of disjoint members of $\kappa (\Omega)$ have disjoint neighborhoods.