Whitney’s Extension Problem in O-minimal Structures
نویسنده
چکیده
In 1934, H. Whitney asked how one can determine whether a real-valued function on a closed subset of Rn is the restriction of a Cm-function on Rn. 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 C1-case of Whitney’s Extension Problem in this context. Our main tool is a definable version of Michael’s Selection Theorem, and we include other another applications of this theorem, to solving linear equations in the ring of definable continuous functions.
منابع مشابه
Whitney’s Extension Theorem in O-minimal Structures
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 pro...
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