The intersection number of real polynomial mappings

Let X = V ( f 1 , … , f n − m ) ⊂ R n be a compact real algebraic set and g : X → R 2 m be a continuous function. If the diagonal in X × X is isolated in the set of self-intersection points of g, we define the intersection number of g. In the case where X is a manifold and g is an immersion it is the intersection number defined by Whitney. In the case where g is a polynomial mapping, we present an effective formula for this number.