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Let $\Omega$ be an open subset of $\mathbb R^n$, with $\Omega \neq \emptyset$ and $\Omega \neq \mathbb R^n$.

Can you give an example where $\partial\Omega \neq \partial\bar{\Omega}$, and how can one exclude this situation?

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    a) disk minus a radius; b) assume that the boundary is a smooth surface.2012-05-24

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