Local algebraic approximation of semianalytic sets
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- by M. Ferrarotti, E. Fortuna and L. Wilson PDF
- Proc. Amer. Math. Soc. 143 (2015), 13-23 Request permission
Abstract:
Two subanalytic subsets of $\mathbb {R}^n$ are called $s$-equivalent at a common point $P$ if the Hausdorff distance between their intersections with the sphere centered at $P$ of radius $r$ vanishes to order $>s$ when $r$ tends to $0$. In this paper we prove that every $s$-equivalence class of a closed semianalytic set contains a semialgebraic representative of the same dimension. In other words any semianalytic set can be locally approximated to any order $s$ by means of a semialgebraic set and hence, by previous results, also by means of an algebraic one.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): July 10, 2012
- Received by editor(s) in revised form: January 16, 2013, January 18, 2013, and February 25, 2013
- Published electronically: September 3, 2014
- Additional Notes: The first and second authors’ research was partially supported by M.I.U.R. and by G.N.S.A.G.A
- Communicated by: Daniel Ruberman
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 13-23
- MSC (2010): Primary 14P15, 32B20, 32S05
- DOI: https://doi.org/10.1090/S0002-9939-2014-12212-X
- MathSciNet review: 3272727