On smooth locally o-minimal functions

zbMath1325.32007MaRDI QIDQ491440

Andreas Fischer

Publication date: 25 August 2015

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ijm/1436275484

zbMATH Keywords

subanalytic setslocal definabilitylocally definable diffeomorphy

Mathematics Subject Classification ID

Semialgebraic sets and related spaces (14P10) Semi-analytic sets, subanalytic sets, and generalizations (32B20) Model theory of ordered structures; o-minimality (03C64)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(p\)-adic and real subanalytic sets
• On Efroymson's extenson theorem for Nash functions
• Semianalytic and subanalytic sets
• Classification of Nash manifolds
• The elementary theory of restricted analytic fields with exponentiation
• Analytic stratification in the Pfaffian closure of an \(o\)-minimal structure
• Approximation theorems in o-minimal structures
• Geometric categories and o-minimal structures
• A theorem of the complement and some new o-minimal structures
• An o-minimal structure which does not admit \(\mathcal C^{\infty}\) cellular decomposition
• Smooth functions in o-minimal structures
• Differentiable manifolds
• The Field of Reals with Multisummable Series and the Exponential Function
• Transition maps at non-resonant hyperbolic singularities are o-minimal
• Abstract Nash Manifolds
• Approximation Theorems for Nash Mappings and Nash Manifolds
• A generalization of the Tarski-Seidenberg theorem, and some nondefinability results
• The real field with convergent generalized power series
• The Pfaffian closure of an o-minimal structure
• On defining C^∞
• Exponentiation is Hard to Avoid
• Quasianalytic Denjoy-Carleman classes and o-minimality
• Infinite Differentiability in Polynomially Bounded O-Minimal Structures
• Quasi-analytic solutions of analytic ordinary differential equations and o-minimal structures
• Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function

This page was built for publication: On smooth locally o-minimal functions