关于三维凸多面体的补作为${\mathbb R}^3$的多项式象
On the complements of 3-dimensional convex polyhedra as polynomial images of ${\mathbb R}^3$
摘要：
证明了三维凸多面体${\mathcal K}\subset{\mathbb R}^3$的补${\mathcal S}:={\mathbb R}^3\setminus{\mathcal K}$及其闭包$\overline{\mathcal S}$是${\mathbb R}^3$的多项式象.前一种技术一般不能扩展到将这样的半代数集${\mathcal S}$和$\overline{\mathcal S}$表示为${\mathbb R}^n$的多项式映象，如果$n\geq4$。
英文摘要：
We prove that the complement ${\mathcal S}:={\mathbb R}^3\setminus{\mathcal K}$ of a 3-dimensional convex polyhedron ${\mathcal K}\subset{\mathbb R}^3$ and its closure $\overline{\mathcal S}$ are polynomial images of ${\mathbb R}^3$. The former techniques cannot be extended in general to represent such semialgebraic sets ${\mathcal S}$ and $\overline{\mathcal S}$ as polynomial images of ${\mathbb R}^n$ if $n\geq4$.
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