Configurations in and coproducts of Priestley spaces
Priestley spaces are compact ordered order separated spaces; the famous Priestley duality links the resulting category with that of distributive lattices. The behaviour of finite connected subposets (configurations) in such a space reflects in algebraic, sometimes well-defined, properties of the corresponding lattice.
Configurations in coproducts of Priestley spaces (suitable - and not yet completely understood - compactifications of their disjoint sums) are not necessarily inherited from the configurations of the summands, and this phenomenon is connected with the above mentioned lattice links. The situation will be explained.
Also, a few open problems will be mentioned, including a possibly Godel-type theorem characterizing acyclic configurations.
Ales Pultr (Charles Univ., Prague, Czech Republic)
April 22, 2008