Projective Fraïssé limits of trees with confluent epimorphisms

Abstract

We continue the study of projective Fraïssé limits developed by Irwin-Solecki and Panagiotopoulos-Solecki by investigating families of epimorphisms between finite trees and finite rooted trees. Ideas of monotone, confluent, and light mappings from continuum theory as well as several properties of continua are modified so as to apply them to topological graphs. As the topological realizations of the projective Fraïssé limits we obtain the dendrite $D_3$, the Mohler-Nikiel universal dendroid, as well as new, interesting continua for which we do not yet have topological characterizations.

A very preliminary version of this work is in arXiv:2212.05167