2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69330Nested 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.8 pagesCombinatorics06A11; 05E25, 32S45, 57N80text