A DUAL ADJOINTNESS ON PARTIALLY ORDERED TOPOLOGICAL-SPACES

The spectral dual adjoint between the mixed category X of the category of partially ordered sets and the category of convergence spaces and that of distributive lattices with 0 and 1 formed over X has been constructed by Hong and Nel. They have extended the Priestley duality. In this paper, another spectral dual adjoint has been constructed by the use of simple topological convergences, rather than by the use of the structures of convergence spaces. It is shown that this adjunction is an extension of the Banaschewski duality. Further, another kind of Priestley type duality is obtained.