Let $A$ and $B$ be sets such that $A\subset \overline B$ and $B \subset \overline A$.
Isn't that an equivalent statement to saying that $A$ is dense in the closure of $B$ and that $B$ is dense in the closure of $A$? And
What is the technical name for a set $A$ being dense in the closure of $B$ and vice versa, as with $\mathbb{Q}$ and the irrationals?