Polynomial images of R-n

Abstract

Let R be a real closed field and n greater than or equal to 2. We prove that: (1) for every finite subset F of R", the semialgebraic set R"\F is a polynomial image of R"; and (2) for any independent linear forms 1, of R", the semialgebraic set {l(1) > 0,..., l(r) > 0} subset of R" is a polynomial image of R"