An o-minimal structure which does not admit \(C^\infty\) cellular decomposition

DOI10.5802/aif.2439zbMath1193.03065OpenAlexW2321265448MaRDI QIDQ1013022

Olivier Le Gal, Jean-Philippe Rolin

Publication date: 29 April 2009

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2009__59_2_543_0

zbMATH Keywords

o-minimalsmooth cell decomposition

Mathematics Subject Classification ID

Singularities of differentiable mappings in differential topology (57R45) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27) Model theory of ordered structures; o-minimality (03C64)

Related Items (9)

Approximation of o-minimal maps satisfying a Lipschitz condition ⋮ A generic condition implying o-minimality for restricted \(C^\infty\)-functions ⋮ Transversality of smooth definable maps in O-minimal structures ⋮ On the points realizing the distance to a definable set ⋮ Construction of O-minimal Structures from Quasianalytic Classes ⋮ Theorem of Lion and o-minimal structures which do not admit $\mathcal {C}^{\infty }$-cell decompositions ⋮ Approximations in globally subanalytic and Denjoy-Carleman classes ⋮ Cohomology of flat currents on definable pseudomanifolds ⋮ Bounding the length of gradient trajectories

Cites Work

• Unnamed Item
• \(p\)-adic and real subanalytic sets
• Semianalytic and subanalytic sets
• Complements of subanalytic sets and existential formulas for analytic functions
• A theorem of the complement and some new o-minimal structures
• The Field of Reals with Multisummable Series and the Exponential Function
• The real field with convergent generalized power series
• Quasianalytic Denjoy-Carleman classes and o-minimality

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