Algebraic approximation of germs of real analytic sets
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- by M. Ferrarotti, E. Fortuna and L. Wilson PDF
- Proc. Amer. Math. Soc. 138 (2010), 1537-1548 Request permission
Abstract:
Two subanalytic subsets of $\mathbb {R}^n$ are $s$-equivalent at a common point, say $O$, if the Hausdorff distance between their intersections with the sphere centered at $O$ of radius $r$ goes to zero faster than $r^s$. In the present paper we investigate the existence of an algebraic representative in every $s$-equivalence class of subanalytic sets. First we prove that such a result holds for the zero-set $V(f)$ of an analytic map $f$ when the regular points of $f$ are dense in $V(f)$. Moreover we present some results concerning the algebraic approximation of the image of a real analytic map $f$ under the hypothesis that $f^{-1}(O)=\{O\}$.References
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Additional Information
- M. Ferrarotti
- Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
- Email: ferrarotti@polito.it
- E. Fortuna
- Affiliation: Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, I-56127 Pisa, Italy
- Email: fortuna@dm.unipi.it
- L. Wilson
- Affiliation: Department of Mathematics, University of Hawaii, Manoa, Honolulu, Hawaii 96822
- Email: les@math.hawaii.edu
- Received by editor(s): January 9, 2009
- Published electronically: January 19, 2010
- Additional Notes: This research was partially supported by M.I.U.R. and by G.N.S.A.G.A
- Communicated by: Daniel Ruberman
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1537-1548
- MSC (2000): Primary 14P15, 32B20, 32S05
- DOI: https://doi.org/10.1090/S0002-9939-10-10283-4
- MathSciNet review: 2587437