Projective Fra\"iss\'e limits of trees with confluent epimorphisms

TL;DR

This paper extends the study of projective Fra"issé limits to finite trees with confluent epimorphisms, revealing new continua including the dendrite D_3 and the Mohler-Nikiel universal dendroid.

Contribution

It introduces new classes of topological graphs as limits of finite trees with confluent epimorphisms, expanding the understanding of their topological properties.

Findings

Identification of the dendrite D_3 as a projective Fra"issé limit.

Construction of the Mohler-Nikiel universal dendroid as a limit.

Discovery of new continua with unknown topological characterizations.

Abstract

We continue the study of projective Fra\"iss\'e 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 Fra\"iss\'e 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.