Weierstrass division theorem in definable $C^{∞}$ germs in a polynomially bounded o-minimal structure

• Autorzy: Abdelhafed Elkhadiri , Hassan Sfouli
• Języki publikacji: EN

Abstrakty

EN

We give some examples of polynomially bounded o-minimal expansions of the ordered field of real numbers where the Weierstrass division theorem does not hold in the ring of germs, at the origin of ℝⁿ, of definable $C^{∞}$ functions.

Kategorie tematyczne

• 26E05: Real-analytic functions
• 03C50: Models with special properties (saturated, rigid, etc.)
• 03C65: Models of other mathematical theories
• 26E10: C ∞ -functions, quasi-analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2006
• Tom: 89
• Numer: 2
• Strony: 127-137

Daty

wydano

2006

Twórcy

autor

Abdelhafed Elkhadiri

• Department of Mathematics, Faculty of Sciences, University Ibn Tofail, BP 133 Kénitra, Morocco

autor

Hassan Sfouli

• Department of Mathematics, Faculty of Sciences, University Ibn Tofail, BP 133 Kénitra, Morocco

Identyfikatory

DOI

10.4064/ap89-2-2