  Let g:X -> Y be a smooth (i.e. C^\infty differentiable) map between two
smooth manifolds. In analogy with the case of complex polynomial functions, we
say that y_0 in Y is a typical value of g if there exists an open neighbourhood
U of y_0 in Y, such that the restriction g:g^{-1}(U) -> U is a C^\infty trivial
fibration. If y_0 in Y is not a typical value of g, then y_0 is called an
atypical value of g. We denote by B_g the bifurcation set of g, i.e. the set of
atypical values of g. In the case of a complex polynomial function f:C^n -> C
it is known that B_f is a finite set. It was previously proved that the
bifurcation sets of real polynomial functions are also finite.
  The aim of this note is to show that the bifurcation set B_f of a smooth
definable function f:R^n -> R is finite .
