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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
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 $\ C^{\ast }(\mathbb{R})$.
📌 3 Key Takeaways
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Objective & Hypothesis:Let$\ X$ be a locally compact and noncompact$\ G-$space with a compact group $G$.
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Key Findings & Data: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 $X$.
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Conclusion & Impact: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 $\ C^{\ast }(\mathbb{R})$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Gelfand compactification · one-point compactification · orbit space
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 $\ C^{\ast }(\mathbb{R})$.
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Cite This Article
KARAPINAR, D., ÖZKURT, A. A. (2019). A description for the compactification of the orbit space. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 4, 2025–2031. https://ajindex.com/articles/212735