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Compactification of a noncompact regular level set of a map $\Bbb R^n\to \Bbb R$
Consider a smooth function $f:\Bbb R^n\to \Bbb R$, and a noncompact regular level subset $S=f^{-1}(c)$ for some regular value $c\in \Bbb R$. Then $S$ is a smooth hypersurface in $\Bbb R^n$, so it is ...