Polynomial images of Rn

✍ Scribed by José F. Fernando; J.M. Gamboa

• Book ID: 104152556
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 229 KB
• Volume: 179
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(02)00121-4

✦ Synopsis

Let R be a real closed ÿeld and n ¿ 2. We prove that: (1) for every ÿnite 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 l1; : : : ; lr of R n , the semialgebraic set {l1 ¿ 0; : : : ; lr ¿ 0} ⊂ R n is a polynomial image of R n .