Submission date: 22 September 2013.

Abstract:

In 1934, H. Whitney asked how one can determine whether a real-valued function on a closed subset of euclidean space is the restriction of an m-times continuously differentiable function. A complete answer to this question was found much later by C. Fefferman in the early 2000s. Here, we work in an o-minimal expansion of a real closed field and solve the C^1-case of Whitney's Extension Problem in this context.

Mathematics Subject Classification: 54C65, 03C64

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