Submission date: 22 September 2013.

Abstract:

In 1934, Whitney gave a necessary and sufficient condition on a jet of order m on a closed subset E of euclidean space to be the jet of order m of an m-times continuously differentiable function; jets satisfying this condition are known as C^m-Whitney fields. Later, Pawlucki and Kurdyka proved that subanalytic C^m-Whitney fields are jets of order m of sybanalytic C^m-functions. Here, we work in an o-minimal expansion of a real closed field and prove a definable version of Whitney's Extension Theorem: every definable C^m-Whitney field is a jet of order m of a definable C^m-function.

Mathematics Subject Classification: 03C64

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