Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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EVERY DEFINABLE Cr MANIFOLD IS AFFINE

  • KAWAKAMI, TOMOHIRO (Department of Mathematics, Faculty of Education, Wakayama University)
  • Published : 2005.02.01
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Abstract

Let M = (R, +, $\cdot$, <, ... ) be an o-minimal expansion of the standard structure R = (R, +, $\cdot$, >) of the field of real numbers. We prove that if 2 $\le$ r < $\infty$, then every n-dimensional definable $C^r$ manifold is definably $C^r$ imbeddable into $R^{2n+l}$. Moreover we prove that if 1 < s < r < $\infty$, then every definable $C^s$ manifold admits a unique definable $C^r$ manifold structure up to definable $C^r$ diffeomorphism.

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References

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Cited by

  1. Smooth functions in o-minimal structures vol.218, pp.2, 2008, https://doi.org/10.1016/j.aim.2008.01.002