  We show that every $\mu$-constant family of isolated hypersurface
singularities of type f(x) + tg(x), where t is a parameter, is topologically
trivial. In the proof we construct explicitely a vector field trivializing the
family. The proof uses only the curve selection lemma and hence, for an
appropriately translated statement, also works over the reals. Some
applications to the study of singularities at infinity of complex polynomials
are given.
