RT Journal Article T1 A note on a separation problem A1 Ruiz Sancho, Jesús María AB The author proves the following theorem: Let A0 be a closed 1-dimensional semianalytic germ at the origin 0∈Rn. Let Z be a semianalytic set in Rn whose germ Z0 at 0 is closed and A0∩Z0={0}. Then there exists a polynomial h∈R[x1,⋯,xn] such that h∣Z∖{0}>0 and h∣A0∖{0}<0. The proof is by induction on the number of blowing-ups needed to "solve" the set A0. Some implications are then given, in particular a similar result for semialgebraic sets in Rn and polynomials. PB Birkhäuser Verlag SN 0003-889X YR 1984 FD 1984 LK https://hdl.handle.net/20.500.14352/64767 UL https://hdl.handle.net/20.500.14352/64767 LA eng NO G. W. BRUMFIEL, Some open problems, in Ordered fields and real algebraic geometry. Contemporary Math. 8, Amer. Math. Soc. (1982).S. LOJASIEWICZ, Ensembles semi-analytiques. Lecture Notes 1965 at I.H.E.S., Bures-sur-Yvette; reproduit n. 466.765, Ecole Polythecnique, Paris.T. MOSTOWSKI, Some properties of the ring of Nash functions. Ann. Scuola Norm. Sup. Pisa, III, 243-266 (1976).J. J. RISLER, Sur le théoreme des fonctions composées différentiables. Ann. Institut Fourier, 32 (2), 229-260 (1982).J. M. RUIZ, Central orderings in fields of real meromorphic function germs. Manuscripta Math. 46, 1-3, 193-214 (1984). DS Docta Complutense RD 7 dic 2023