Araştırma Makalesi
BibTex RIS Kaynak Göster

On $\mu$-paracompact and $\mu$-expandable spaces

Yıl 2025, Cilt: 8 Sayı: 2, 85 - 92, 19.10.2025
https://doi.org/10.33773/jum.1595789

Öz

We introduced $(\mu,\kappa)$-perfect mapping and $\mu$-expandable space in generalized topology as well as  characterized. Also give an example that there exists a $\mu$-paracompact and $\mu$-$T_{2}$ space which is not $\mu$-regular. Finally, we proved some results on preserving the image (pre-image) of $\mu$-paracompact and $\mu$-expandable space.

Kaynakça

  • Császár, Á. (1997). Generalized open sets. Acta Mathematica Hungarica, 75, 65–87.
  • Császár, Á. (2002). Generalized topology, generalized continuity. Acta Mathematica Hungarica, 96, 351– 357.
  • Arar, M. (2014). A note on spaces with a countable μ-base. Acta Mathematica Hungarica, 144, 494–498.
  • Arar, M. (2016). On countably μ-paracompact spaces. Acta Mathematica Hungarica, 149, 50–57.
  • Abd El-Monsef, M. E., El-Deeb, S. N., & Mahmoud, R. A. (1983). β-open sets and β-continuous mappings. Bulletin of the Faculty of Science, Assiut University, 12, 77–90.
  • Al-Zoubi, K. (2004). s-expandable spaces. Acta Mathematica Hungarica, 102 (3), 203–210.
  • Al-Jarrah, H. H., & Al Zoubi, K. Y. (2019). P-expandable spaces. Italian Journal of Pure and Applied Mathematics, 41 (3), 497–507.
  • De Arruda Saraiva, L. E. (2011). Generalized quotient topologies. Acta Mathematica Hungarica, 132, 168–173.
  • Demir, I., & Ozbakir, O. B. (2013). β-expandable spaces. Filomat, 27 (6), 971–976.
  • Krajewski, L. L. (1971). On expanding locally finite collections. Canadian Journal of Mathematics, 23 (1), 58–68.
  • Levine, N. (1963). Semi-open sets and semi-continuity in topological spaces. The American Mathematical Monthly, 70 (1), 36–41.
  • Mashhour, A. S., Abd El-Monsef, M. E., & El-Deeb, S. N. (1982). On precontinuous and weak precontinuous mappings. Proceedings of the Mathematical and Physical Society of Egypt, 53, 47–53.
  • Njastad, O. (1965). On some classes of nearly open sets. Pacific Journal of Mathematics, 15 (3), 961–970.
  • Sarkar, N., Das, A., & Aman, T. E. (2023). When an operator gives a unique generalized topology. Journal of Linear and Topological Algebra, 12, 97–104.
  • Ray, A. D., & Bhowmick, R. (2014). μ-paracompact and μ-paracompact generalized topological spaces. Hacettepe Journal of Mathematics and Statistics, 45 (2), 447–453.
  • Sarsak, M. S. (2013). On μ-compact sets in μ-spaces. Questions and Answers in General Topology, 31, 49–57.
  • Zuhier, A., & Jawarneh, I. (2022). μ-countably compactness and μH-countably compactness. Communications of the Korean Mathematical Society, 37 (1), 269–277.

On $\mu$-paracompact and $\mu$-expandable spaces

Yıl 2025, Cilt: 8 Sayı: 2, 85 - 92, 19.10.2025
https://doi.org/10.33773/jum.1595789

Öz

We introduced $(\mu,\kappa)$-perfect mapping and $\mu$-expandable space in generalized topology as well as  characterized. Also give an example that there exists a $\mu$-paracompact and $\mu$-$T_{2}$ space which is not $\mu$-regular. Finally, we proved some results on preserving the image (pre-image) of $\mu$-paracompact and $\mu$-expandable space.

Kaynakça

  • Császár, Á. (1997). Generalized open sets. Acta Mathematica Hungarica, 75, 65–87.
  • Császár, Á. (2002). Generalized topology, generalized continuity. Acta Mathematica Hungarica, 96, 351– 357.
  • Arar, M. (2014). A note on spaces with a countable μ-base. Acta Mathematica Hungarica, 144, 494–498.
  • Arar, M. (2016). On countably μ-paracompact spaces. Acta Mathematica Hungarica, 149, 50–57.
  • Abd El-Monsef, M. E., El-Deeb, S. N., & Mahmoud, R. A. (1983). β-open sets and β-continuous mappings. Bulletin of the Faculty of Science, Assiut University, 12, 77–90.
  • Al-Zoubi, K. (2004). s-expandable spaces. Acta Mathematica Hungarica, 102 (3), 203–210.
  • Al-Jarrah, H. H., & Al Zoubi, K. Y. (2019). P-expandable spaces. Italian Journal of Pure and Applied Mathematics, 41 (3), 497–507.
  • De Arruda Saraiva, L. E. (2011). Generalized quotient topologies. Acta Mathematica Hungarica, 132, 168–173.
  • Demir, I., & Ozbakir, O. B. (2013). β-expandable spaces. Filomat, 27 (6), 971–976.
  • Krajewski, L. L. (1971). On expanding locally finite collections. Canadian Journal of Mathematics, 23 (1), 58–68.
  • Levine, N. (1963). Semi-open sets and semi-continuity in topological spaces. The American Mathematical Monthly, 70 (1), 36–41.
  • Mashhour, A. S., Abd El-Monsef, M. E., & El-Deeb, S. N. (1982). On precontinuous and weak precontinuous mappings. Proceedings of the Mathematical and Physical Society of Egypt, 53, 47–53.
  • Njastad, O. (1965). On some classes of nearly open sets. Pacific Journal of Mathematics, 15 (3), 961–970.
  • Sarkar, N., Das, A., & Aman, T. E. (2023). When an operator gives a unique generalized topology. Journal of Linear and Topological Algebra, 12, 97–104.
  • Ray, A. D., & Bhowmick, R. (2014). μ-paracompact and μ-paracompact generalized topological spaces. Hacettepe Journal of Mathematics and Statistics, 45 (2), 447–453.
  • Sarsak, M. S. (2013). On μ-compact sets in μ-spaces. Questions and Answers in General Topology, 31, 49–57.
  • Zuhier, A., & Jawarneh, I. (2022). μ-countably compactness and μH-countably compactness. Communications of the Korean Mathematical Society, 37 (1), 269–277.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Topoloji
Bölüm Araştırma Makalesi
Yazarlar

Nırmal Sarkar 0000-0002-9050-1479

Towhıd Aman 0000-0003-4027-1422

Ashoke Das 0000-0002-6612-0182

Yayımlanma Tarihi 19 Ekim 2025
Gönderilme Tarihi 3 Aralık 2024
Kabul Tarihi 31 Ağustos 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 8 Sayı: 2

Kaynak Göster

APA Sarkar, N., Aman, T., & Das, A. (2025). On $\mu$-paracompact and $\mu$-expandable spaces. Journal of Universal Mathematics, 8(2), 85-92. https://doi.org/10.33773/jum.1595789
AMA Sarkar N, Aman T, Das A. On $\mu$-paracompact and $\mu$-expandable spaces. JUM. Ekim 2025;8(2):85-92. doi:10.33773/jum.1595789
Chicago Sarkar, Nırmal, Towhıd Aman, ve Ashoke Das. “On $\mu$-paracompact and $\mu$-expandable spaces”. Journal of Universal Mathematics 8, sy. 2 (Ekim 2025): 85-92. https://doi.org/10.33773/jum.1595789.
EndNote Sarkar N, Aman T, Das A (01 Ekim 2025) On $\mu$-paracompact and $\mu$-expandable spaces. Journal of Universal Mathematics 8 2 85–92.
IEEE N. Sarkar, T. Aman, ve A. Das, “On $\mu$-paracompact and $\mu$-expandable spaces”, JUM, c. 8, sy. 2, ss. 85–92, 2025, doi: 10.33773/jum.1595789.
ISNAD Sarkar, Nırmal vd. “On $\mu$-paracompact and $\mu$-expandable spaces”. Journal of Universal Mathematics 8/2 (Ekim2025), 85-92. https://doi.org/10.33773/jum.1595789.
JAMA Sarkar N, Aman T, Das A. On $\mu$-paracompact and $\mu$-expandable spaces. JUM. 2025;8:85–92.
MLA Sarkar, Nırmal vd. “On $\mu$-paracompact and $\mu$-expandable spaces”. Journal of Universal Mathematics, c. 8, sy. 2, 2025, ss. 85-92, doi:10.33773/jum.1595789.
Vancouver Sarkar N, Aman T, Das A. On $\mu$-paracompact and $\mu$-expandable spaces. JUM. 2025;8(2):85-92.