Let A be a closed semialgebraic subset of Euclidean space of codimension at least one, and containing the origin 0 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.
Local approximation of semialgebraic sets
FORTUNA, ELISABETTA;
2002-01-01
Abstract
Let A be a closed semialgebraic subset of Euclidean space of codimension at least one, and containing the origin 0 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.File in questo prodotto:
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