On quasi-orbital space

Abstract

Let G be a subgroup of the group Homeo(E) of homeomorphisms of a Hausdorff topological space E. The class of an orbit O of G is the union of all orbits having the same closure as O. We denote by E/ G the space of classes of orbits called quasi-orbit space. A space X is called a quasi-orbital space if it is homeomorphic to E/ G where E is a compact Hausdorff space. In this paper, we show that every infinite second countable quasi-compact T0-space is the quotient of a quasiorbital space.2010 MSC: 54F65; 54H20.