Real Algebraic and Analytic Geometry |

Polynomial images of R^n.

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Submission: 2002, April 25.

*Abstract:
Let R be a real closed field and n>=2.
We prove that: (1) for every finite subset F of R^n, the semialgebraic set R^n\ F is a polynomial
image of R^n; and (2) for any independent linear forms l_1,...,l_r of R^n,
the semialgebraic subset {l_1>0,...,l_r>0} of R^n is a polynomial image of R^n.*

Mathematics Subject Classification (2000): 14P10, 14Q99.

Keywords and Phrases: polynomial images, real closed field, semialgebraic set, quadrant.

**Full text**, 16p.:
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