Degree of homogeneity on cones

Abstract

MSC: 54B15 54F15 54F50 Keywords: 1 2 -homogeneous 1 n -homogeneous Cone Continuum Degree of homogeneity Local dendrite OrbitThe degree of homogeneity of a space X is the number of orbits for the action of the group of homeomorphisms of X onto itself. In this paper we determine the degree of homogeneity of the cone of a space X in terms of that of X, in the case in which X is either a local dendrite or a Hausdorff space with no arcs.