We continue the study of projective Fraisse limits developed by Irwin-Solecki and Panagiotopoulos-Solecki by investigating families of epimorphisms between finite trees and finite rooted trees. We focus on particular classes of epimorphisms such as monotone, confluent or simple confluent, which are adaptations to graphs of monotone or confluent maps from continuum theory. As the topological realizations of the projective Fraisse limits we obtain the dendrite \(D_3\) the Mohler-Nikiel universal dendroid, as well as new, interesting compact connected spaces (continua) for which we do not yet have topological characterizations.
The talk is based on joint work with Charatonik, Roe, Yang.