Let $\Omega\subseteq\mathbb{R}^n$ be an open set. If $x\in\overline{\Omega}$ Can I always find such a sequence $\{x_n\}\subseteq\Omega$ such that $x_n\to x$?
I believe such a result exists, but I don't remember if the hypotheses and why it can be done.
Could anyone help me?