On All Kinds of Homogeneous Spaces

Abstract

Several open questions on homogeneous spaces are answered.A few of the results are:(1) An -homogeneous metric continuum, which is not the circle, is strongly -homogeneous.(2) A 2-homogeneous metric continuum is locally connected.(3) If A1 is a homogeneous compact metric space or a homogeneous locally compact, locally connected separable metric space, then X is a coset space.(4) If G is a complete separable metric topological group with is -connected, then G is locally -connected.