1/2-Homogeneity of nth suspensions

A space is said to be 1 2 -homogeneous provided that there are exactly two orbits for the action of the group of homeomorphisms of the space onto itself. Certain conditions on a continuum X are known under which the suspension over X is 1 2 -homogeneous [17]. In this paper we determine sufficient conditions under which the nth suspension of a Hausdorff space is 1 2 -homogeneous.