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Let be a closed semialgebraic subset of euclidean space of codimension at least one, and containing the origin as a non-isolated point. We prove that, for every real , there exists an algebraic set which approximates to order at . The special case generalizes the result of the authors that every semialgebraic cone of codimension at least one is the tangent cone of an algebraic set.
@article{ASNSP_2002_5_1_1_1_0,
author = {Ferrarotti, Massimo and Fortuna, Elisabetta and Wilson, Les},
title = {Local approximation of semialgebraic sets},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {1--11},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 1},
number = {1},
year = {2002},
mrnumber = {1994799},
zbl = {1051.14065},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_1_0/}
}
TY - JOUR AU - Ferrarotti, Massimo AU - Fortuna, Elisabetta AU - Wilson, Les TI - Local approximation of semialgebraic sets JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2002 SP - 1 EP - 11 VL - 1 IS - 1 PB - Scuola normale superiore UR - http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_1_0/ LA - en ID - ASNSP_2002_5_1_1_1_0 ER -
%0 Journal Article %A Ferrarotti, Massimo %A Fortuna, Elisabetta %A Wilson, Les %T Local approximation of semialgebraic sets %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2002 %P 1-11 %V 1 %N 1 %I Scuola normale superiore %U http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_1_0/ %G en %F ASNSP_2002_5_1_1_1_0
Ferrarotti, Massimo; Fortuna, Elisabetta; Wilson, Les. Local approximation of semialgebraic sets. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_1_0/