Subordinations on Bounded Distributive Lattices

CELANI, SERGIO A.

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS

SPRINGER

Año: 2022

0167-8094

In this paper we shall study some classes of bounded distributive lattices endowed with a subordination relation, called subordination lattices. We shall prove that certain algebraic conditions defined in terms of subordinations correspond to first-order conditions on the dual space of a subordination lattice. As a consequence of these correspondences we shall obtain new topological dualities for some known classes of subordination lattices, as for instance the class of proximity lattices studied by M. B. Smyth, or the class of strong proximity lattices studied by A. Jung and P. Sünderhauf. We shall also introduce some new classes of subordination lattices, as the class of compingent lattices and de Vries lattices.