Incidence structures and Stone-Priestley duality

Details Incidence structures and Stone-Priestley duality Incidence structures and Stone-Priestley duality

2006-01-06

arxiv.org/abs/math/0601121v1

Mathematics

Combinatorics

14 pages

Scientific paper

We observe that if $R:=(I,\rho, J)$ is an incidence We observe that if $R:=(I,\rho, J)$ 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.

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