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In this paper we introduce the notion of modified Nash triviality for a family of zero sets of real polynomial map-germs as a desirable one. We first give a Nash isotopy lemma which is a useful tool to show triviality.
Then, using it, we prove two types of modified Nash triviality theorem and a finite classification theorem for this triviality. These theorems strengthen similar topological results.
We show that a subanalytic map-germ (Rⁿ,0) → (Rⁿ,0) which is arc-analytic and bi-Lipschitz has an arc-analytic inverse.
In this paper we construct non-trivial examples of isomorphisms and
we obtain, via toric modifications, an inverse function theorem in this category. We also
show that any analytic curve in , can be deformed via a rational blow-
analytic isomorphism of , to a smooth analytic arc.
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