w-dependance et dépendance générale au sens de Marczewski
Weierstrass division theorem in definable germs in a polynomially bounded o-minimal structure
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 functions.
Weierstrass division theorem in quasianalytic local rings
The main result of this paper is the following: if the Weierstrass division theorem is valid in a quasianalytic differentiable system, then this system is contained in the system of analytic germs. This result has already been known for particular examples, such as the quasianalytic Denjoy-Carleman classes.
Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions