On $\mu$-paracompact and $\mu$-expandable spaces
Yıl 2025,
Cilt: 8 Sayı: 2, 85 - 92, 19.10.2025
Nırmal Sarkar
,
Towhıd Aman
,
Ashoke Das
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
Nırmal Sarkar
,
Towhıd Aman
,
Ashoke Das
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.