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=eG 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=eG where E is a compact Hausdorff space. In this paper, we show that every in nite second countable quasi-compact T0-space is the quotient of a quasi-orbital space.

Keywords

• homeomorphism
• group
• quasi-orbit space
• quasi-orbital space.