Local approximation of semialgebraic sets
Massimo Ferrarotti; Elisabetta Fortuna; Les Wilson
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)
- Volume: 1, Issue: 1, page 1-11
- ISSN: 0391-173X
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topFerrarotti, Massimo, Fortuna, Elisabetta, and Wilson, Les. "Local approximation of semialgebraic sets." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.1 (2002): 1-11. <http://eudml.org/doc/84464>.
@article{Ferrarotti2002,
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 $s\ge 1$, 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.},
author = {Ferrarotti, Massimo, Fortuna, Elisabetta, Wilson, Les},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {semialgebraic sets; proximity; Hausdorff distance; tangent cone},
language = {eng},
number = {1},
pages = {1-11},
publisher = {Scuola normale superiore},
title = {Local approximation of semialgebraic sets},
url = {http://eudml.org/doc/84464},
volume = {1},
year = {2002},
}
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
PB - Scuola normale superiore
VL - 1
IS - 1
SP - 1
EP - 11
AB - 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 $s\ge 1$, 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.
LA - eng
KW - semialgebraic sets; proximity; Hausdorff distance; tangent cone
UR - http://eudml.org/doc/84464
ER -
References
top- [B-C-R] J. Bochnak – M. Coste – M. F. Roy, “Géométrie algébrique réelle”, Springer-Verlag, 1987. Zbl0633.14016MR949442
- [B1] L. Bröcker, Families of semialgebraic sets and limits, In: “Real Algebraic Geometry” (Rennes 1991), M. Coste – L. Mahé – M.-F. Roy (eds.), Lecture Notes in Math., 1524, Springer-Verlag, Berlin, 1992, pp. 145-162. Zbl0849.14022MR1226248
- [B2] L. Bröcker, On the reduction of semialgebraic sets by real valuations, in: “Recent advances in real algebraic geometry and quadratic forms”, Contemp. Math., 155, Amer. Math. Soc., Providence, RI, 1994, pp. 75-95. Zbl0826.14038MR1260702
- [F-F-W] M. Ferrarotti – E. Fortuna – L. Wilson, Real algebraic varieties with prescribed tangent cones, Pacific J. Math. 194 (2000), 315-323. Zbl1036.14027MR1760783
- [K-R] K. Kurdyka – G. Raby, Densité des ensembles sous-analytiques, Ann. Inst. Fourier (Grenoble) 39 (1989), 753-771. Zbl0673.32015MR1030848
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