Archivio Istituzionale della RicercaLet A be a closed semialgebraic subset of Euclidean space of codimension at least one, and containing the origin O as a non–isolated point. We prove that, for every real s ≥ 1, there exists an algebraic set V which approximates A to order s at O. The special case s = 1 generalizes the result of the authors that every semialgebraic cone of codimension at least one is the tangent cone of an algebraic set.
Approximation of subanalytic sets by normal cones / Ferrarotti, Massimo; Fortuna, E.; Wilson, L.. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - 39:(2007), pp. 247-254. [10.1112/blms/bdl034]
Approximation of subanalytic sets by normal cones
FERRAROTTI, Massimo;
2007
Abstract
Let A be a closed semialgebraic subset of Euclidean space of codimension at least one, and containing the origin O as a non–isolated point. We prove that, for every real s ≥ 1, there exists an algebraic set V which approximates A to order s at O. The special case s = 1 generalizes the result of the authors that every semialgebraic cone of codimension at least one is the tangent cone of an algebraic set.
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https://hdl.handle.net/11583/1529475
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