Real Algebraic and Analytic Geometry
Submission: 2007, April 23.
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.
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