Projective Fra\"iss\'e limits and generalized Wa\.zewski dendrites
Abstract
We continue the study of projective Fra\"iss\'e limits of trees initiated by Charatonik and Roe and we construct many generalized Wa\.zewski dendrites as the topological realization of a projective Fra\"iss\'e limit of families of finite trees with (weakly) coherent epimorphisms. Moreover we use the categorical approach to Fra\"iss\'e limits developed by Kubi\'s to construct all generalized Wa\.zewski dendrites as topological realizations of Fra\"iss\'e limits of suitable categories of finite structures. As an application we recover a homogeneity result for countable dense sets of endpoints in generalized Wa\.zewski dendrites.
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