Abstract
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 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.
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Bekkali, M., Pouzet, M. & Zhani, D. Incidence structures and Stone–Priestley duality. Ann Math Artif Intell 49, 27–38 (2007). https://doi.org/10.1007/s10472-007-9059-0
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DOI: https://doi.org/10.1007/s10472-007-9059-0