Smooth functions in o-minimal structures |
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Authors: | Andreas Fischer |
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Institution: | University of Saskatchewan, Department of Mathematics and Statistics, Saskatoon, SK, S7N 5E6, Canada |
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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 C1-diffeomorphic. |
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Keywords: | Smooth functions o-Minimal structure Differentiable manifolds |
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