On compactifications of an orbit space

Abstract

One of the important research topics in the theory of topological transformation groups is to examine the relationships between the topological properties of a G-space X and the orbit space X/G. In [19], Srivastava studied the relationship between the Stone-Cech

compactification of a completely regular space and the Stone-Cech
compactification of the orbit space. A similar study was done for the Hewitt
realcompactification in [7].

In this paper, we obtain that the c-realcompactification of the orbit
space X/G is homeomorfic to the orbit space of the c-realcompactification of X, when G is a finite discrete group and X is a completely regular G-space. We will also show a similar result for almost realcompactification.