Weierstrass division theorem in definable $C^{\infty}$ germs in a polynomially bounded o-minimal structure
Volume 89 / 2006
Annales Polonici Mathematici 89 (2006), 127-137
MSC: Primary 03C50, 26E10; Secondary 26E05, 03C65.
DOI: 10.4064/ap89-2-2
Abstract
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 $\mathbb{R}^n$, of definable $C^{\infty}$ functions.
