  Nested set complexes appear as the combinatorial core of De Concini-Procesi
arrangement models. We show that nested set complexes are homotopy equivalent
to the order complexes of the underlying meet-semilattices without their
minimal elements. For atomic semilattices, we consider the realization of
nested set complexes by simplicial fans as proposed in math.AG/0305142 by the
first author and S. Yuzvinsky. We show that in this case the nested set
complexes in fact are homeomorphic to the mentioned order complexes.
