  We consider a spherically symmetric distribution of dust and show that it is
possible, under general physically reasonable conditions, for an overdensity to
evolve to an underdensity (and vice versa). We find the conditions under which
this occurs and illustrate it on a class of regular Lemaitre-Tolman-Bondi
solutions. The existence of this phenomenon, if verified, would have the result
that the topology of density contours, assumed fixed in standard structure
formation theories, would have to change and that luminous matter would not
trace the dark matter distribution so well.
