  We study the topology of analytic families of $n$-dimensional complex
hypersurfaces having an isolated singularity at the origin. We prove that such
a family is $\mu$-constant if and only if it admits an uniform Milnor radius,
which happens if and only if it has constant embedded topological type. In
particular, this solves the $\mu$-constant problem, formulated by D.T. L\^e and
C.P. Ramanujam in 1976.
