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Let $K\subset \mathbb{R}^n$ be a closed set, then is there existing a smooth function $f\in C^{\infty}(\mathbb{R}^n,\mathbb{R})$, such that $ (1)\quad f\ge 0, $ $ (2) \quad f^{-1}(0)=K. $

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    @HaraldHanche-Olsen Yes (now I can't edit the commnet anymore).2012-10-12

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