Also the notion of continuity of functions between formal spaces is reduced to pointfree terms, that is to the notion of morphisms of formal topologies. A survey on formal topology is in preparation. The First Workshop on Formal Topology has been held in Padova, October 2 - 4, 1997. The notions of open and closed subsets are naturally defined by means of the relation itself and so topology can be described as the first generalization of sets. The basic picture is a framework where the pointwise and the pointfree approach to topology can live together.
Basic pairs reveal to be the simplest structures where a notion of continuity can be introduced.
Considering relations instead of functions, continuity becomes a synonym of commutative diagrams.