Smooth functions in o-minimal structures

@article{Fischer2008SmoothFI,
  title={Smooth functions in o-minimal structures},
  author={Andreas Fischer},
  journal={Advances in Mathematics},
  year={2008},
  volume={218},
  pages={496-514}
}
  • A. Fischer
  • Published 2008
  • Mathematics
  • Advances in Mathematics
Abstract Fix an o -minimal expansion of the real exponential field that admits smooth cell decomposition. We study the density of definable smooth functions in the definable continuously differentiable functions with respect to the definable version of the Whitney topology. This implies that abstract definable smooth manifolds are affine. Moreover, abstract definable smooth manifolds are definably C ∞ -diffeomorphic if and only if they are definably C 1 -diffeomorphic. 
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TLDR
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In the present paper we elaborate an o-minimal de Rham cohomology theory for abstract-definable $\mathcal{C}^p$ manifolds with $1\leq p\leq \infty$ in an o-minimal expansion of the real field whichExpand
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