Displaying similar documents to “Algebraic approximation of analytic sets definable in an o-minimal structure”

On the Kuratowski convergence of analytic sets

Maciej P. Denkowski, Rafał Pierzchała (2008)

Annales Polonici Mathematici

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We discuss some conditions which guarantee that the Kuratowski limit of a sequence of analytic sets is a Nash set.

Extending analyticK-subanalytic functions

Artur Piękosz (2004)

Open Mathematics

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Letg:U→ℝ (U open in ℝn) be an analytic and K-subanalytic (i. e. definable in ℝanK, whereK, the field of exponents, is any subfield ofℝ) function. Then the set of points, denoted Σ, whereg does not admit an analytic extension is K-subanalytic andg can be extended analytically to a neighbourhood of Ū.

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...

Separation of global semianalytic sets

Hamedou Diakite (2009)

Annales Polonici Mathematici

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Given global semianalytic sets A and B, we define a minimal analytic set N such that Ā∖N and B̅∖N can be separated by an analytic function. Our statement is very similar to the one proved by Bröcker for semialgebraic sets.

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 .