Let $d\in\mathbb N$ and $\Omega\subseteq\mathbb R^d$ be open. Is there some continuous $\phi:\Omega\to\mathbb R$ with compact support $\operatorname{supp}$ and $\operatorname{supp}\phi=\overline{\Omega}$?
Let $d\in\mathbb N$ and $\Omega\subseteq\mathbb R^d$ be open. Is there some continuous $\phi:\Omega\to\mathbb R$ with compact support $\operatorname{supp}$ and $\operatorname{supp}\phi=\overline{\Omega}$?
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