Submission date: 29 January 2018

Abstract:

Let M=(R, +, × , <, e^x, ...) be an exponential o-minimal expansion of the standard structure R=(R, +, × , <) of the field of real numbers with C^{∞} cell decomposition. We prove that every n-dimensional definable C^{∞} manifold is definably C^{∞} imbeddable into bR^{2n+1}.

Mathematics Subject Classification: 14P10, 14P20, 57R55, 58A05, 03C64.

Keywords and phrases: Definable C^{∞} manifolds, o-minimal, affine.

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