caa a22 4500 463187326 CHVBK 20180406164857.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s10472-007-9059-0 doi (NATIONALLICENCE)springer-10.1007/s10472-007-9059-0 Incidence structures and Stone-Priestley duality [Elektronische Daten] [Mohamed Bekkali, Maurice Pouzet, Driss Zhani] 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. Springer Science+Business Media B.V., 2007 Incidence structure nationallicence Galois lattice nationallicence Boolean algebra nationallicence Distributive lattice nationallicence Bekkali Mohamed Département de Mathématiques, Faculté des Sciences et Techniques, Université Sidi Mohamed Ben Abdellah, B. P. 2202, Saïss-Fès, Morocco aut Pouzet Maurice PCS, Université Claude-Bernard Lyon1, Domaine de Gerland -bât. Recherche [B], 50 avenue Tony-Garnier, 69365, Lyon cedex 07, France aut Zhani Driss Département de Mathématiques, Faculté des Sciences et Techniques, Université Sidi Mohamed Ben Abdellah, B. P. 2202, Saïss-Fès, Morocco aut Annals of Mathematics and Artificial Intelligence Springer Netherlands 49/1-4(2007-04-01), 27-38 1012-2443 49:1-4<27 2007 49 10472 https://doi.org/10.1007/s10472-007-9059-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10472-007-9059-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bekkali Mohamed Département de Mathématiques, Faculté des Sciences et Techniques, Université Sidi Mohamed Ben Abdellah, B. P. 2202, Saïss-Fès, Morocco aut NATIONALLICENCE 700 1- Pouzet Maurice PCS, Université Claude-Bernard Lyon1, Domaine de Gerland -bât. Recherche [B], 50 avenue Tony-Garnier, 69365, Lyon cedex 07, France aut NATIONALLICENCE 700 1- Zhani Driss Département de Mathématiques, Faculté des Sciences et Techniques, Université Sidi Mohamed Ben Abdellah, B. P. 2202, Saïss-Fès, Morocco aut NATIONALLICENCE 773 0- Annals of Mathematics and Artificial Intelligence Springer Netherlands 49/1-4(2007-04-01), 27-38 1012-2443 49:1-4<27 2007 49 10472 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer