[For the entire collection see Zbl 0514.00010.]
A classical problem is to characterize a given ordered algebraic structure by means of a topological space. For Boolean algebras the solution to this problem was given by M. H. Stone in 1937. For distributive lattices the Stone topological representation theorem of 1937 closely imitated his representation theorem for Boolean algebras and made use of a \(T_ 0\) topology. More recently, another simpler topological representation theory for distributive lattices has been given by H. A. Priestley. In this second version the representation space is required to be an ordered topological space with a Hausdorff topology and the Birkhoff representation of a distributive lattice of finite length as the lattice of increasing subsets of a finite ordered set and the duality between finite bounded distributive lattices and finite ordered sets are obtained. Orthomodular lattices have known an increased interest, and a lot of papers have been devoted, in particular, to the study of this structure from the algebraic point of view. Thus the purpose of this paper.