A description for the compactification of the orbit space

Abstract

Let X be a locally compact and noncompact G􀀀space with a compact group G. In this paper, we givesome useful description of a compactification of the orbit space X/G when it is an orbit space of a G􀀀compactificationof X. As an application, we show that the closed bounded interval [a; b] is homeomorphic to the space of maximal idealswith Stone topology of uniformly continuous even functions subring of C(R) .