Dendrites with a countable closure of the set of end points

Abstract

We investigate the problem of existence of universal elements in some families of dendrites with a countable closure of the set of end points. In particular, we prove that for each integer κ 3 and for each ordinal α 1 there exists a universal element in the family of all dendrites X such that ord( X) κ and the α-derivative of the set cl X E( X) contains at most one point.