2006/01/06 by Mohamed Bekkali, Bekkali, Mohamed, Maurice Pouzet +3
Computer Science · #Advanced Algebra and Logic #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.math/0601121
We observe that if R:=(I,ρ, J) is an incidence We observe that if R:=(I,ρ, J) is an incidence structure, viewed as a matrix, then the topological closure of the set of columns is the Stone space of the Boolean algebra generated by the rows. As a consequence, we obtain that the topological closure of the collection of principal initial segments of a poset P is the Stone space of the Boolean algebra Tailalg (P) generated by the collection of principal final segments of P, the so-called \it tail-algebra of P. Similar results concerning Priestley spaces and distributive lattices are given. A generalization to incidence structures valued by abstract algebras is considered.