Let $\bar D $ and $\bar E$ denote the closures of $D$ and $E$ respectively. If $ D\subset \mathbb R^n$, $E \subset \mathbb R^n$ and they are strongly separated. Show that $\bar D $ and $\bar E$ can also be separated strongly.
I got stuck with this proof. I want to use the strong separation proof but I don't know which step to take. Thank you for your help.