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Preprint Number 626
626. A. Thamrongthanyalak Whitney's Extension Theorem in ominimal structures Email: 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 mtimes continuously differentiable function; jets satisfying this condition are known as C^mWhitney fields. Later, Pawlucki and Kurdyka proved that subanalytic C^mWhitney fields are jets of order m of sybanalytic C^mfunctions. Here, we work in an ominimal expansion of a real closed field and prove a definable version of Whitney's Extension Theorem: every definable C^mWhitney field is a jet of order m of a definable C^mfunction. Mathematics Subject Classification: 03C64 Keywords and phrases: Full text: pdf.

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