Vol. 97, No. 2, 1981

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Second note on Artin’s solution of Hilbert’s 17th problem. Order spaces

D. W. Dubois

Vol. 97 (1981), No. 2, 357–371
Abstract

We consider real varieties in Kn∕k, where K∕k is maximally ordered and k is dense in K. Our principal results are:

Theorem 1. Assume V is irreducible. A. The closure of the set of all simple points equals the set of all central points — z V is central if some order of k(V )∕k contains every function which is positive at z. B. If f + r is totally positive in k(V )∕k for every positive r in k, then f itself is totally positive.

Theorem 2. For a semi-algebraic set S in Kn defined by polynomial relations bj(x) = 0, gi(x) > 0 (1 i,j m), define B = (b1,,bm), G = {g1,,gm}. Then every irreducible component of V k(B) contains central points on S if and only if () for 0 < pi k, gij G, ai k[X], ipiΠjgij ai2 R√ --
B implies every ai R√ --
B.

Mathematical Subject Classification 2000
Primary: 12D15
Secondary: 12J15, 14G30
Milestones
Received: 25 June 1980
Published: 1 December 1981
Authors
D. W. Dubois