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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?

Jack J.
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  • This is one way to define closure. If you have another definition this is a theorem. See https://math.stackexchange.com/questions/3593186/what-closure-of-a-given-subset-really-is/3593194#3593194 – Ethan Bolker Apr 22 '20 at 14:50
  • Thanks, but ${x_n}\subseteq\Omega$ or ${x_n}\subseteq\overline{\Omega}$? – Jack J. Apr 22 '20 at 15:32
  • Every point in the closure of a set (whether the set is itself open or closed or neither) is the limit of a sequence of points in the set. – Ethan Bolker Apr 22 '20 at 15:39

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