  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.
