Real Algebraic and Analytic Geometry Preprint Server

e-mail: , ,

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.: pdf 1939k.