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Uniform Linear Bound in Chevalley's Lemma

Published:2008-08-01
Printed: Aug 2008
• E. Bierstone
• P. D. Milman
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Abstract

We obtain a uniform linear bound for the Chevalley function at a point in the source of an analytic mapping that is regular in the sense of Gabrielov. There is a version of Chevalley's lemma also along a fibre, or at a point of the image of a proper analytic mapping. We get a uniform linear bound for the Chevalley function of a closed Nash (or formally Nash) subanalytic set.
 Keywords: Chevalley function, regular mapping, Nash subanalytic set
 MSC Classifications: 13J07 - Analytical algebras and rings [See also 32B05] 32B20 - Semi-analytic sets and subanalytic sets [See also 14P15] 13J10 - Complete rings, completion [See also 13B35] 32S10 - Invariants of analytic local rings

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