RT Journal Article
T1 On global Nash functions
A1 Ruiz Sancho, Jesús María
A1 Shiota, Masahiro
AB Let M superset-of R be a compact Nash manifold, and N (M) [resp. O(M)] its ring of global Nash (resp. analytic) functions. A global Nash (resp. analytic) set is the zero set of finitely many global Nash (resp. analytic) functions, and we have the usual notion of irreducible set. Then we say that separation holds for M if every Nash irreducible set is analytically irreducible. The main result of this paper is that separation holds if and only if every semialgebraic subset of M described by s global analytic inequalities can also be described by s global Nash inequalities. In passing, we also prove that when separation holds, every Nash function on a Nash set extends to a global Nash function on M.
PB Société Mathématique de France
SN 0012-9593
YR 1994
FD 1994
LK https://hdl.handle.net/20.500.14352/57910
UL https://hdl.handle.net/20.500.14352/57910
LA eng
NO DGICYT
DS Docta Complutense
RD 17 abr 2025