A compactification of an orbit space

Abstract

Let X be a Tychonoff G-space, G be a finite discrete group and A be a dense and invariant subspace of X. In this paper, by means of Gelfand's method, we construct a compactification of the orbit space A/G which is homeomorphic a compact G-space. As an application, we show that, the set of maximal ideals of even function ring with Stone topology is a compactification of positive rationals.