A general character theory for partially ordered sets and lattices

We use characters of lattices (i.e. lattice morphisms into
the two element lattice 2) and characters of topological spaces
(i.e. continuous functions into an appropriately topologized two
element space 2) to obtain connections and dualities between
various categories of lattices and topological spaces. The
objective is to present a unified treatment of various known
aspects in the relation between lattices and topological spaces
and to discover, on the way, some new ones.