A description for the compactification of the orbit space

Authors: DÜNYA KARAPINAR, ALİ ARSLAN ÖZKURT

Abstract: Let$\ X$ be a locally compact and noncompact$\ G-$space with a compact group $G$. In this paper, we give some useful description of a compactification of the orbit space $X/G$ when it is an orbit space of a $G-$compactification of $X$. As an application, we show that the closed bounded interval $[a,b]$ is homeomorphic to the space of maximal ideals with Stone topology of uniformly continuous even functions subring of $\ C^{\ast }(\mathbb{R})$.

Keywords: Gelfand compactification, one-point compactification, orbit space, continuous and bounded functions ring

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