Displaying similar documents to “Topological types of fewnomials”

A decomposition of a set definable in an o-minimal structure into perfectly situated sets

Wiesław Pawłucki (2002)

Annales Polonici Mathematici

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A definable subset of a Euclidean space X is called perfectly situated if it can be represented in some linear system of coordinates as a finite union of (graphs of) definable 𝓒¹-maps with bounded derivatives. Two subsets of X are called simply separated if they satisfy the Łojasiewicz inequality with exponent 1. We show that every closed definable subset of X of dimension k can be decomposed into a finite family of closed definable subsets each of which is perfectly situated and such...

A generic condition implying o-minimality for restricted C ∞ -functions

Olivier Le Gal (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove that the expansion of the real field by a restricted C ∞ -function is generically o-minimal. Such a result was announced by A. Grigoriev, and proved in a different way. Here, we deduce quasi-analyticity from a transcendence condition on Taylor expansions. This then implies o-minimality. The transcendance condition is shown to be generic. As a corollary, we recover in a simple way that there exist o-minimal structures that doesn’t admit analytic cell decomposition, and that there...

Invariance of domain in o-minimal structures

Rafał Pierzchała (2001)

Annales Polonici Mathematici

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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.

Extending Tamm's theorem

Lou van den Dries, Chris Miller (1994)

Annales de l'institut Fourier

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We extend a result of M. Tamm as follows: Let f : A → ℝ , A ⊆ ℝ m + n , be definable in the ordered field of real numbers augmented by all real analytic functions on compact boxes and all power functions x ↦ x r : ( 0 , ∞ ) → ℝ , r ∈ ℝ . Then there exists N ∈ ℕ such that for all ( a , b ) ∈ A , if y ↦ f ( a , y ) is C N in a neighborhood of b , then y ↦ f ( a , y ) is real analytic in a neighborhood of b .