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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 $s \geq 1$ , 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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