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Stone style duality for distributive nearlattices. (English) Zbl 1301.06030

Summary: The aim of this paper is to study the variety of distributive nearlattices with greatest element. We will define the class of \(N\)-spaces as sober-like topological spaces with a basis of open, compact, and dually compact subsets satisfying an additional condition. We will show that the category of distributive nearlattices with greatest element whose morphisms are semi-homomorphisms is dually equivalent to the category of \(N\)-spaces with certain relations, called \(N\)-relations. In particular, we give a duality for the category of distributive nearlattices with homomorphisms. Finally, we apply these results to characterize topologically the one-to-one and onto homomorphisms, the subalgebras, and the lattice of the congruences of a distributive nearlattice.

MSC:

06D50 Lattices and duality
06D75 Other generalizations of distributive lattices
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