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