Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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IMBEDDINGS OF MANIFOLDS DEFINED ON AN 0-MINIMAL STRUCTURE ON (R,+,.,<)

  • Kawakami, Tomohiro (Department of mathematics, Faculty of Education, Wakayama University)
  • Published : 1999.02.01
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Abstract

Let M be an 0-minimal structure on the standard structure :=( , +, ,<) of the field of real numbers. We study Cr -G manifolds (0$\leq$r$\leq$w) which are generalizations of Nash manifolds and Nash G manifolds. We prove that if M is polynomially bounded, then every Cr -G (0$\leq$r<$\infty$) manifold is Cr -G imbeddable into some n, and that if M is exponential and G is a compact affine Cw -G group, then each compact $C\infty$ -G imbeddable into some representation of G.

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References

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