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2026-03-29 11:50:09.1774785009
Is it possible to represent an open and connected set in $(\mathbb{R}^n,||\cdot||)$ as the finite union of convex sets?
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No. Take, for instance$$\mathbb{R}^2\setminus\bigcup_{n\in\mathbb{Z}}\bigl(\{n\}\times[0,\infty)\bigr).$$