
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 $\displaystyle (X,\Omega)$ is a $\displaystyle T_1$ space and that:
If $\displaystyle H$ and $\displaystyle K$ are disjoint members of $\displaystyle \kappa (\Omega)$, then there exist $\displaystyle U \in \Omega$ such that $\displaystyle H\subseteq U$ and $\displaystyle \bar{U}\cap K = \emptyset$.
I need to prove that:
Each pair of disjoint members of $\displaystyle \kappa (\Omega)$ have disjoint neighborhoods.