Andradas Heranz, Carlos and Díaz-Cano Ocaña, Antonio
(2004)
*On Marshall’s p-invariant for semianalytic set germs.*
In
Contribuciones matemáticas : homenaje al profesor Enrique Outerelo Domínguez.
Complutense, Madrid, pp. 21-32.
ISBN 8474917670

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## Abstract

The invariant p(V ) has been introduced by M. Marshall as a measure of the complexity of semialgebraic sets of a real algebraic variety V . This invariant is defined as the least integer such that every semialgebraic set S ⊂ V has a

separating family with p(V ) polynomials.

In this paper we provide estimates for the invariant p in the case of analytic set germs. One of the tools we use is a realization theorem which is interesting by itself.

Item Type: | Book Section |
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Uncontrolled Keywords: | Separating familie; Semianalytic germs; Semialgebraic sets. |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 17191 |

References: | C. Andradas, L. Brocker, J. Ruiz: Constructible sets in real geometry. Ergeb.Math. 33, Springer-Verlag, Berlin 1996. C. Andradas, A. Dıaz–Cano: Closed stability index of excellent henselian local rings. To appear in Math. Z.. E. Becker: On the real spectrum of a ring and its application to semialgebraic geometry. Bulletin AMS 15 (1986), 19–60. E. Bierstone, P.D. Milman: Local resolution of singularities. Lecture Notes in Math. 1420 (1990), 42–64. J. Bochnak, M. Coste, M.F. Roy: Real algebraic geometry. Ergeb. Math. 36,Springer-Verlag, Berlin 1998. L. Brocker: On basic semialgebraic sets. Expo. Math. 9 (1991), 289–334. Spaces of orderings and semialgebraic sets. Can. Math. Soc. Conf.Proc. 4 (1984), 231–248. M. Marshall: Separating families for semialgebraic sets. Manuscripta math.80 (1993), 73–79. Quotients and inverse limits of spaces of orderings. Can. J. Math.31 (1979), 604–616. J.M. Ruiz: A note on a separation problem. Arch. Math. 43 (1984), 422–426. |

Deposited On: | 23 Nov 2012 12:00 |

Last Modified: | 07 Feb 2014 09:43 |

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