An uncountable family of monotone homogeneous dendrites

Janusz J. Charatonik, Wrocław, Poland

Keywords: dendrite, homogeneous, mapping, monotone, standard, universal AMS Subject classification: 54C10, 54F50

Abstract: H. Kato has shown in [4] and [5] that the standard universal dendrite D_{3} of order 3 is homogeneous with respect to monotone mappings. The result has later been generalized in [1] by showing that for each m ∈ {3, 4, …, ≤} the standard universal dendrite D_{m} of order m has the discussed property. In this paper these results are extended to all standard universal dendrites D_{S}, where S is an arbitrary nonempty subset of {3, 4, …, ≤}.