...bounded distributive lattices with Galois connections in...
A lattice L is weakly atomic if, given x<y in L, there exist a,b∈L such that x⩽a≺b⩽y, where ≺ denotes the covering relation of L. A complete lattice L satisfies the join-infinite distributive law if for any S⊆L and x∈L,(JID)x∧(⋁S)=⋁{x∧y|y∈S}. Th...