Bounded distributive lattice expansions - Gehrke, Mai; Jónsson, Bjarni (Mathematica Scandinavica, 2004)
A new notion of a canonical extension A^σ is introduced that applies to arbitrary bounded distributive lattice expansions (DLEs) A . The new definition agrees with the earlier ones whenever they apply. In particular, for a bounded distributive lattice A, A^σ has the same meaning as before. A novel feature is the introduction of several topologies on the universe of the canonical extension of a DL. One of these topologies is used to define the canonical extension f^σ :A^σ → B^σ of an arbitrary map f:A→ B between DLs, and hence to define the canonical extension A^σ of an arbitrary DLE A. Together the topologies form a powerful tool for showing that many properties of DLEs are preserved by canonical extensions.