Algebraic approximation of germs of real analytic sets

Authors:
M. Ferrarotti, E. Fortuna and L. Wilson

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

Published electronically:
January 19, 2010

MathSciNet review:
2587437

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Abstract: Two subanalytic subsets of are -equivalent at a common point, say , if the Hausdorff distance between their intersections with the sphere centered at of radius goes to zero faster than . In the present paper we investigate the existence of an algebraic representative in every -equivalence class of subanalytic sets. First we prove that such a result holds for the zero-set of an analytic map when the regular points of are dense in . Moreover we present some results concerning the algebraic approximation of the image of a real analytic map under the hypothesis that .

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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

DOI:
https://doi.org/10.1090/S0002-9939-10-10283-4

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

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.