International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 8, Pages 447-453

Mathematical morphology and poset geometry

Alain Bretto1 and Enzo Maria Li Marzi2

1University of Saint-Etienne, LIGIV, Site G.I.A.T Industries 3, Rue Javelin Pagnon, BP 505, Saint-Etienne Cedex 1 42007, France
2Department of Mathematics, University of Messina, Contrada Papardo, Salita Sperone 31 98166 Sant'Agata, Messina, Italy

Received 16 February 2001

Copyright © 2001 Alain Bretto and Enzo Maria Li Marzi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this paper is to characterize morphological convex geometries (resp., antimatroids). We define these two structures by using closure operators, and kernel operators. We show that these convex geometries are equivalent to poset geometries.