Stratification structures on a kind of completely distributive lattices and their applications in theory of topological molecular lattices

A completely distributive lattice is also called a molecular lattice.The least and the greatestelements in a lattice are denoted by 0 and 1,respectively.For the empty subset L of alattice L,we assume that V=0 and ∧=1.The set of all the molecules(i.e.non-zero∨-irreducible elements)in a lattice L is denoted by M(L). Let Land Lbe completely distributive lattices,f:L→Land g:L→Lbe order-preserving maps.If for any a∈Land any b∈L,f(a)≤b if and only if a≤g(b),then fis called the left adjoint of g,or g is called the right adjoint of f.The right adjoint of f is