A Linear Extension Operator for Whitney Fields on Closed O-minimal Sets

We construct a natural continuous linear extension operator for CWhitney fields (p finite) on closed o-minimal subsets, different from the Whitney’s one [W], based on the geometry of these sets. Introduction. By an o-minimal subset of an Euclidean space R we will mean a subset definable in any o-minimal structure on the ordered field of real numbers R (see [D, DM] for the definition and fundamental properties). We refer the reader to [W], [G], [M], [S] or/and [T] for basic facts on Whitney fields. It will be convenient for us to adopt the following definition of a Whitney field. Let p ∈ N \ {0} and let A be a locally closed subset of R; i.e. contained and closed in some open subset G ⊂ R. A Cp-Whitney field on A is a polynomial