Stone style duality for distributive nearlattice

SERGIO CELANI AND ISMAEL CALOMINO

ALGEBRA UNIVERSALIS

BIRKHAUSER VERLAG AG

Lugar: BASEL; Año: 2014

0002-5240

TThe 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.