A note on Bierstone-Milman-Pawłucki's paper

Krzysztof Jan Nowak

Displaying similar documents to “A note on Bierstone-Milman-Pawłucki's paper 'Composite differentiable functions'”

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.

On the implicit function theorem in o-minimal structures

Zofia Ambroży, Wiesław Pawłucki (2015)

Banach Center Publications

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A local-global version of the implicit function theorem in o-minimal structures and a generalization of the theorem of Wilkie on covering open sets by open cells are proven.

Quasiadditivity of capacity and minimal thinness.

Aikawa, Hiroaki (1993)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

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A generic condition implying o-minimality for restricted C $^{\infty}$ -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 $^{\infty}$ -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...

Fiberwise properties of definable sets and functions in o-minimal structures.

P. Speissegger (1995)

Manuscripta mathematica

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Michael's theorem for Lipschitz cells in o-minimal structures

Małgorzata Czapla, Wiesław Pawłucki (2016)

Annales Polonici Mathematici

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A version of Michael's theorem for multivalued mappings definable in o-minimal structures with M-Lipschitz cell values (M a common constant) is proven. Uniform equi-LCⁿ property for such families of cells is checked. An example is given showing that the assumption about the common Lipschitz constant cannot be omitted.

On the minimal overlap problem of Erdös

L Moser (1959)

Acta Arithmetica

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Minimal realcompact spaces

Asit Baran-Raha (1972)

Colloquium Mathematicae

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Minimal Niven numbers

H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)

Acta Arithmetica

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A multidimensional Taylor's theorem with minimal hypothesis

J. Marshall Ash, A. Eduardo Gatto, Stephen Vági (1990)

Colloquium Mathematicae

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Division of Distributions by Locally Definable Quasianalytic Functions

Krzysztof Jan Nowak (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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We demonstrate that the Łojasiewicz theorem on the division of distributions by analytic functions carries over to the case of division by quasianalytic functions locally definable in an arbitrary polynomially bounded, o-minimal structure which admits smooth cell decomposition. Hence, in particular, the principal ideal generated by a locally definable quasianalytic function is closed in the Fréchet space of smooth functions.

Minimal cell coverings of sphere bundles over spheres

Daniel A. Moran (1975)

Commentationes Mathematicae Universitatis Carolinae

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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 $f : A \to ℝ, A \subseteq ℝ^{m + n}$ , be definable in the ordered field of real numbers augmented by all real analytic functions on compact boxes and all power functions $x \mapsto x^{r} : (0, \infty) \to ℝ, r \in ℝ$ . Then there exists $N \in ℕ$ such that for all $(a, b) \in A$ , if $y \mapsto f (a, y)$ is $C^{N}$ in a neighborhood of $b$ , then $y \mapsto f (a, y)$ is real analytic in a neighborhood of $b$ .