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

Dendrites with a countable closure of the set of end points

“…The set of end points of this universal dendrite is homeomorphic to a Cantor ternary set. Some results concerning the existence of universal elements in the families of dendrites with a closed countable set of end points are in [7]. In particular, it is shown that in the family of all dendrites with a closed countable set of end points there is no universal element.…”

“…We begin with construction, for a fixed integer κ 3, of a tree X κ m of order κ that contains a copy of any tree of order κ with at most m ramification points (see [7]). For any integer κ 1 by κ-od with center p, we refer to any union of κ arcs having p as one end point and disjoint out of p.…”