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In this paper we prove the implicit function theorem for , and as an interesting application of using blow-analytic homeomorphisms, we
describe a very easy way to resolve singularities of analytic curves.
Let be a set-germ at such that . We say that is a direction of at if there is a sequence of points tending to such that as . Let denote the set of all directions of at .
Let be subanalytic set-germs at such that . We study the problem of whether the dimension of the common direction set, is preserved by bi-Lipschitz homeomorphisms. We show that although it is not true in general, it is preserved if the images of and are also subanalytic. In particular...
We show that a subanalytic map-germ (Rⁿ,0) → (Rⁿ,0) which is arc-analytic and bi-Lipschitz has an arc-analytic inverse.
In a previous paper by Koike and Paunescu, it was introduced the notion of direction set for a subset of a Euclidean space, and it was shown that the dimension of the common direction set of two subanalytic subsets, called , is preserved by a bi-Lipschitz homeomorphism, provided that their images are also subanalytic. In this paper we give a generalisation of the above result to sets definable in an o-minimal structure on an arbitrary real closed field. More precisely, we first prove our main theorem...
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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