Duality for Bounded Lattices
نویسنده
چکیده
We present a duality theorem for bounded lattices that improves and strengthens Urquhart's topological representation for lattices. Rather than using maximal, disjoint lter-ideal pairs, as Urquhart does, we use all disjoint lter-ideal pairs. This allows not only for establishing a bijective correspondance between lattices and a certain kind of doubly ordered Stone Spaces (Urquhart), but for a full duality result. We provide, in the sequel, a treatment of congruences and epimorphisms, as well as of sublattices, proving relevant duality theorems. The paper is concluded with a sectional representation of lattices, imbedding a general lattice in a sheaf space of lattices.
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تاریخ انتشار 1993