Projective Fraïssé limits of trees with confluent epimorphisms

2023/12/28 by Włodzimierz J. Charatonik, Aleksandra Kwiatkowska, Charatonik, Włodzimierz J. +5
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Mathematical Dynamics and Fractals #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2312.16915

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 D₃, the Mohler-Nikiel universal dendroid, as well as new, interesting continua for which we do not yet have topological characterizations.

Related

• Projective Fra"ıssé limits of trees
• Projective Fraïssé limits and generalized Ważewski dendrites
• The projective Fra"ıssé limit of the family of all connected finite graphs with confluent epimorphisms
• Shapes of infinite conformally balanced trees
• A combinatorial model for the Menger curve