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Journals / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 4

A description for the compactification of the orbit space

Ali Arslan ÖZKURT
Dünya KARAPINAR
Pages
2025–2031
Publication Date
2022-11-04
DOI
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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 idealswith Stone topology of uniformly continuous even functions subring of C(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 givesome useful description of a compactification of the orbit space X/G when it is an orbit space of a G􀀀compactificationof 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 idealswith Stone topology of uniformly continuous even functions subring of C(R) .
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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) .

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Cite This Article

ÖZKURT, A. A., KARAPINAR, D. (2022). A description for the compactification of the orbit space. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 4, 2025–2031. https://ajindex.com/articles/607603

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References (6)

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  2. Gelfand IM, Kolmogorov AN. On rings of continuous functions on topological spaces. Doklady Akademii Nauk SSSR 1939; 22: 11-15
  3. Karapınar D. A compactification of an orbit space. Filomat 2018; 32 (10): 3429-3434
  4. Megrelishvili MG. A Tychonoff G􀀀space not admitting a compact Hausdorff G􀀀extension or G􀀀linearization. Russian Mathematical Surveys 1988; 43 (2): 177-178
  5. Porter JR, Woods RG. Extensions and Absolutes of Hausdorff Spaces. New York, NY, USA: Springer-Verlag, 1988
  6. Srivastava K. On the Stone-Cech compactification of an orbit space. Bulletin of the Australian Mathematical Society 1987; 36: 435-439.