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A note on a separation problem

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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

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


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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
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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