Research announcement on extending Nash functions off singular curves (Q1061800)

In this announcement the author discusses the definition and extension properties of Nash functions on a singular real algebraic set. He gives indications on the proof of the following result: Let V be a Nash curve \(V\subset {\mathbb{R}}^ n\) and f a Nash (i.e. analytic and algebraic) function : \(V\to {\mathbb{R}}\) then f can be extended to \({\mathbb{R}}^ n\). The result is false in the case of dimension 2 (Whitney's umbrella).