  We proof here the existence of a topological thick and thin decomposition of
any closed definable thick isolated singularity germ in the spirit of the
recently discovered metric thick and thin decomposition of complex normal
surface singularities of [10]. Our thin zone catches exactly the homology of
the family of the links collapsing faster than linearly. Simultaneously we
introduce a class of rigid homeomorphisms more general than bi-Lipschitz ones,
which map the topological thin zone onto the topological thin zone of its
image. As a consequence of this point of view for the class of singularities we
consider we exhibit an equivalent description of the notion of separating sets
in terms of this fast contracting homology
