Suppose $A$ and $B$ are sets such that $\overline{A}\cap B = \emptyset = \overline{B}\cap A$. Furthermore, $A$ and $B$ can be written as a countable union of closed sets. I am trying to show that there exist disjoint open sets $U,V$ such that $A$ is in $U$ and $B$ is in $V$. I am not sure where to start.
Note this is all happening in a normal T1 space.
