Submission date: 10 April 2019

Abstract:

We prove a definable version of the Whitney embedding theorem for abstract-definable C^p manifolds with 1 ≤ p< ∞, namely:
every abstract-definable C^p manifold is abstract-definable C^p embedded into R^N, for some positive integer N. As a consequence, we show that every abstract-definable C^p manifold has a compatible c^{p+1} atlas.

Mathematics Subject Classification: 03C64, 12D15, 14Pxx

Keywords and phrases:

Full text arXiv 1904.05403: pdf, ps.