Generalized homogeneity of dendrites
by
Evan P. Wright
Missouri University of Science and Technology

A continuum X is called monotonely homogeneous if, for every pair of points x, y ∈ X, there is a monotone map from X onto itself which takes x to y. A continuum is said to be 1/3-homogeneous if the action of its group of self-homeomorphisms has exactly three orbits. We provide characterizations of these two properties in the class of dendrites.

(Note that the only homogeneous dendrite is a singleton, and the only 1/2-homogeneous dendrite is an arc, so 1/3-homogeneity is the first interesting case).

Date received: February 28, 2008