In this paper we prove the implicit function theorem for locally blow-analytic functions, and as an interesting application of using blow-analytic homeomorphisms, we describe a very easy way to resolve singularities of analytic curves.
On étudie les propriétés métriques des ensembles analytique réels , avec , algèbre analytique topologiquement noethérienne. Ainsi, on construit de larges classes d’algèbres topologiquement noethériennes et vérifiant des conditions de Łojasiewicz globales d’un certain type. Comme application, on obtient des théorèmes de division de fonction par des fonctions analytiques.
Soit une fonction sous-analytique de à valeurs dans Nous montrons que l’intégrale est une fonction log-analytique de Nous en déduisons que le volume -dimensionnel des éléments d’une famille sous-analytique de sous-ensembles sous-analytiques globaux de l’espace euclidien est une fonction log-analytique de Un corollaire de ce résultat est le caractère log-analytique de la fonction densité -dimensionnelle d’un sous-analytique global de dimension en tout point de sa fermeture topologique....
We give a relation between two theories of improper intersections, of Tworzewski and of Stückrad-Vogel, for the case of algebraic curves. Given two arbitrary quasiprojective curves V₁,V₂, the intersection cycle V₁ ∙ V₂ in the sense of Tworzewski turns out to be the rational part of the Vogel cycle v(V₁,V₂). We also give short proofs of two known effective formulae for the intersection cycle V₁ ∙ V₂ in terms of local parametrizations of the curves.
We consider the intersection multiplicity of analytic sets in the general situation. We prove that it is a regular separation exponent for complex analytic sets and so it estimates the Łojasiewicz exponent. We also give some geometric properties of proper projections of analytic sets.
We present a construction of an intersection product of arbitrary complex analytic cycles based on a pointwise defined intersection multiplicity.
The aim of this paper is to prove the theorem on invariance of domain in an arbitrary o-minimal structure. We do not make use of the methods of algebraic topology and the proof is based merely on some basic facts about cells and cell decompositions.
We describe the notion of a weakly Lipschitz mapping on a stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the Verdier condition.
An isolated point of intersection of two analytic sets is considered. We give a sharp estimate of their regular separation exponent in terms of intersection multiplicity and local degrees.