Universal dendrites for some families of dendrites with a countable set of end points

摘要

We prove that for any countable ordinal α ≥ 1 (and for any integer κ ＞ 3), there exists a universal dendrite in the family of all dendrites (of orders ≤ κ) with a closed countable set of end points such that the α-derivative of the set of end points contains at most one point.