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Ruiz Sancho, Jesús María
(1984)
*A note on a separation problem.*
Archiv der Mathematik, 43
(5).
pp. 422-426.
ISSN 0003-889X

PDF
Restringido a Repository staff only 202kB |

Official URL: http://link.springer.com/content/pdf/10.1007%2FBF01193850

## Abstract

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.

Item Type: | Article |
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Uncontrolled Keywords: | Separation problem; semianalytic germ; analytic function germ; semialgebraic sets |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 20293 |

Deposited On: | 06 Mar 2013 15:09 |

Last Modified: | 12 Dec 2018 15:14 |

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