Degree of homogeneity on suspensions

Given a positive integer n, a space is a said to be 1 n -homogeneous provided there are exactly n orbits for the action of the group of homeomorphisms of the space onto itself. In this paper we determine the degree of homogeneity of the suspension of X, in terms of that of X, when X is a local dendrite. Further, we establish which are the orbits of S u s ( X ) and, finally, we show that no dendrite has 1 3 -homogeneous suspension.