Dualities between complete lattices
Juan Enrique Martínez-Legaz, Ivan Singer · Optimization · 1990
We study dualities between two complete lattices Eand Fi.e., mappings △:E→ F satisfying for all {x i } iεI ⊆E and all index sets I including the empty set I = Ø. We give characterizations and representations of dualities △, and some results on the dual △* F→Eof △ and on the associated hull operator △*△:E→Ein the general case and in various particular eases. Among several applications, we devote special attention to Fenchel-Moreau conjugations.