Publication: A note on a separation problem
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Publication Date
1984
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Birkhäuser Verlag
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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.
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