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Order convergence and compactness
Dominic van der Zypen
Let be a partially ordered set and let be a compact topology on that is finer than the interval topology. Then is contained in the order (convergence) topolo…
Remarks on affine complete distributive lattices
Dominic van der Zypen
We characterise the Priestley spaces corresponding to affine complete bounded distributive lattices. Moreover we prove that the class of affine complete bounded distributive lattic…
Representable posets and their order components
Michael E. Adams, Dominic van der Zypen
A partially ordered set P is representable if there is a bounded distributive lattice such that its ordered set of prime ideals is order-isomorphic to P. We show that if the order…
Distributive lattice orderings and Priestley duality
Michel Krebs, Dominic van der Zypen
The ordering relation of a bounded distributive lattice L is a (distributive) (0, 1)-sublattice of L \times L. This construction gives rise to a functor Φfrom the category of bound…