On Compactification of an Orbit Space of Finite Group Action

Abstract

In this work, we studies another construction to the-compactification (Stone-Cech) of a Tychnoff space X which helps us to extend the action on X toX and we prove that:The Stone-Cech (resp., one point) compactification of the orbit space byG , whereG is a finite discrete group of productGXis the orbit of the Stone-Cech (resp., one point) compactification of the product of the G -spaces that is GXG X      ( )(resp., GXG X   ( )( )   ) and with extra conditions we get that ( )GXG X     .