13-homogeneous dendrites

Homogeneity degree of fans

“…We have confined our attention here to fans, as they comprise a simple class of dendroids, and hence make a good starting point for the study of homogeneity degree of dendroids. In the classification of all 1 3 -homogeneous dendrites given in [3], many interesting dendrites appear, including the locally connected fans, the universal (n-branching) dendrites, and the (n-branching) Gehman dendrites. It would be interesting to extend this to a classification of all 1 3 -homogeneous dendroids, perhaps beginning with smooth dendroids.…”

“…This can be seen in recent work, e.g. in the classification of all homogeneous plane continua (more generally compact spaces in the plane) completed in [13], and the classification of all 1 3 -homogeneous dendrites [3]. In this paper we initiate a study of dendroids of low homogeneity degree, beginning with fans.…”