Classes of pretopological spaces closed under the formation of final structures

We investigate coreflective subconstructs of the construct Prtop of pretopological spaces and continuous maps and in particular the inclusion “order” between these subconstructs. We describe the smallest, second and third coreflective class and then all minimal elements that are strictly larger. Using these minimal elements we obtain a “partition” of the whole conglomerate of coreflective subconstructs of Prtop. The results dealing with classes in one member of this partition have an immediate interpretation in the framework of reflexive relations.