Real Algebraic and Analytic Geometry |

Smooth Approximation in O-Minimal Structures.

e-mail:

Submission: 2007, April 23.

*Abstract:
Fix an $o$-minimal expansion of the real exponential field that possesses smooth cell decomposition.
We prove smooth approximation of definable differentiable functions with respect to a
topology closely related to the Whitney topology. As a consequence we obtain a strong version of definable smooth separation of sets,
which we use to prove that definable smooth manifolds are definably affine.*

Mathematics Subject Classification (2000): 03C64, 57R12, 57R40, 57R50, 58A05, 14P99.

Keywords and Phrases: o-minimal structures, exponential function, approximation, smooth cell decomposition, definable manifold.

**Full text**, 15p.:
dvi 79k,
ps.gz 192k,
pdf 242k.

Server Home Page