Countable dense sets of dendrites

Abstract

For each separable space X, we consider the family of all countable dense sets of X modulo an equivalence relation defined as follows: we say that M∼N if and only if there is a homeomorphism h:X→X such that h[M]=N. The countable dense homogeneity degree of X is defined as the cardinality of the set of the equivalence classes under the relation ∼. In case such degree equals 1, the space is said to be countable dense homogeneous. Countable dense homogeneity has become a classical concept and has been studied with interest in the last decades. In this paper we present a full characterization of the countable dense homogeneity degree for the class of dendrites.