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Dergiler / 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
Sayfa
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Yayın Tarihi
2024-12-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this research, we present the notion of statistical compactness restricted up to order $\alpha$, where $\alpha \in (0,1]$.
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Temel Bulgular & Veri:There exist statistically compact spaces that are not compact.
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Sonuç & Katkı:A finite intersection-like characterization for $\alpha$ statistical compactness has also been established.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (16)

  1. Bal, P., Rakshit, D., Sarkar, S.,Countable compactness modulo an ideal of natural numbers, Ural Math. J., 9(2)(2023), 28–35.
  2. Bal, P., De, R.,On strongly star semi-compactness of topological spaces, Khayyam J. Math., 9(2023), 54–60.
  3. Bal, P., Bhowmik, S., On R-star-Lindel¨of Spaces, Palest. J. Math., 6(2)(2017), 480–486.
  4. Bal, P., Bhowmik, S., Gauld, D., On Selectively star-Lindel¨of properties, J. Indian Math. Soc. 85)(3-4(2018), 291–304.
  5. Bal, P., Koˇcinac, Lj.D.R., On Selectively star-ccc spaces, Topology Appl., 281(2020), Art. No. 107184.
  6. Bal, P., Rakshit, D., A variation of the class of statistical γ-covers, Topol. Algebra Appl., 11(2023), Art. No. 20230101.
  7. Bal, P., Sarkar, S., Rakshit, D., On statistical compactness,Iran. J. Math. Sci. Inform., (accepted), 2024.
  8. Bhunia, S., Das, P., Pal, S.K., Restricting statistical convergence, Acta Math. Hungar., 134(2012), 153–161.
  9. Debnath, S., Rakshit, D., On I-statistical convergence, Iran. J. Math. Sci. Inform., 13(2)(2018), 101–109.
  10. Di Maio, G., Koˇcinak, Lj.D.R., Statistical convergence in topology, Topology Appl., 156(1)(2008), 28–45.
  11. Engelking, R., General Topology, Sigma Series in Pure Mathematics, Revised and Complete ed. Berlin: Heldermann, 1989.
  12. Fast, H., Sur la convergence statistique, Colloq. Math., 2(1951), 241–244.
  13. Fridy, J.A., On statistical convergence, Analysis, 5(1985), 301–313.
  14. Koˇcinak, Lj.D.R., Singh, S., On the set version of selectively star-ccc spaces, J. Math., 2020(2020), Art. ID. 9274503.
  15. Mursaleen, M., Debnath, S., Rakshit, D., I-statistical Limit superior and I-statistical limit Inferior, Filomat, 31(7)(2012), 2103–2108.
  16. Schoenberg, I.J., The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(5)(1959), 361–375.