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Journals / Turkish Journal of Mathematics and Computer Science / 2024 / Volume: 16 Issue: 2

Parameterized Statistical Compactness of Topological Spaces

Tanmayee Datta(ICFAI University Tripura)0009-0009-1953-1577
Prasenjit Bal(ICFAI University Tripura)0000-0001-5047-7390
Parthiba Das(ICFAI University Tripura)0009-0000-2191-0327
Pages
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Publication Date
2024-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

A finite intersection-like characterization for $\alpha$ statistical compactness has also been established.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this research, we present the notion of statistical compactness restricted up to order $\alpha$, where $\alpha \in (0,1]$.
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Key Findings & Data:There exist statistically compact spaces that are not compact.
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Conclusion & Impact:A finite intersection-like characterization for $\alpha$ statistical compactness has also been established.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Countable compactness · natural density · finite intersection property.

Abstract

In this research, we present the notion of statistical compactness restricted up to order $\alpha$, where $\alpha \in (0,1]$. There exist statistically compact spaces that are not compact. So the parameter $\alpha$ became the measurement of non compactness. Additionally, we looked for the continued existence of order $\alpha$ statistical compactness under open continuous surjection and sub-space topology. A finite intersection-like characterization for $\alpha$ statistical compactness has also been established.

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Cite This Article

Datta, T., Bal, P., Das, P. (2024). Parameterized Statistical Compactness of Topological Spaces. Turkish Journal of Mathematics and Computer Science, Volume: 16 Issue: 2. https://doi.org/10.47000/tjmcs.1542927

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