Projective Fraïssé limits and generalized Ważewski dendrites
Volume 265 / 2024
Fundamenta Mathematicae 265 (2024), 35-73
MSC: Primary 54D80; Secondary 54F15, 54F50
DOI: 10.4064/fm310-1-2024
Published online: 27 March 2024
Abstract
We continue the study of projective Fraïssé limits of trees initiated by Charatonik and Roe and further continued by Charatonik, Kwiatkowska, Roe and Yang. We construct many generalized Ważewski dendrites as topological realizations of projective Fraïssé limits of families of finite trees with (weakly) coherent epimorphisms. Moreover, we use the categorical approach to Fraïssé limits developed by Kubiś to construct all generalized Ważewski dendrites as topological realizations of Fraïssé limits of suitable categories of finite structures. As an application, we recover a homogeneity result for countable dense sets of endpoints in generalized Ważewski dendrites.
