University of Luxembourg [Luxembourg] (Campus Kirchberg
6, rue Richard Coudenhove-Kalergi
L-1359 Luxembourg
Campus de Limpertsberg
162a, avenue de la Faïencerie
L-1511 Luxembourg
Campus de Belval
2, avenue de l'Université
L-4365 Esch-sur-Alzette - Luxembourg)
Abstract : 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. Conservative Median Algebras and Semilattices. Order, Springer Verlag, 2016, 33 (1), pp.121-132. ⟨10.1007/s11083-015-9356-x⟩. ⟨hal-01175696⟩