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Local approximation of semialgebraic sets

Massimo Ferrarotti;  Elisabetta Fortuna;  Les Wilson — 2002

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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