Conservative median algebras and semilattices
  We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median algebras and certain topological structures, we obtain descriptions of the median-preserving mappings between products of finitely many chains. 
Miguel Couceiro, Jean-Luc Marichal, Bruno Teheux
math.RA