Whitney’s Extension Theorem in O-minimal Structures
نویسنده
چکیده
In 1934, Whitney gave a necessary and sufficient condition on a jet of order m on a closed subset E of R to be the jet of order m of a C-function; jets satisfying this condition are known as C-Whitney fields. Later, Paw lucki and Kurdyka proved that subanalytic C-Whitney fields are jets of order m of sybanalytic C-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-Whitney field is a jet of order m of a definable C-function.
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