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

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.

Anahtar Kelimeler

• Generalized topology
• $\mu$-paracompact
• $\mu$-expandable
• $\mu$-locally finite.

Kaynakça

1. Császár, Á. (1997). Generalized open sets. Acta Mathematica Hungarica, 75, 65–87.
2. Császár, Á. (2002). Generalized topology, generalized continuity. Acta Mathematica Hungarica, 96, 351– 357.
3. Arar, M. (2014). A note on spaces with a countable μ-base. Acta Mathematica Hungarica, 144, 494–498.
4. Arar, M. (2016). On countably μ-paracompact spaces. Acta Mathematica Hungarica, 149, 50–57.
5. 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.
6. Al-Zoubi, K. (2004). s-expandable spaces. Acta Mathematica Hungarica, 102 (3), 203–210.
7. Al-Jarrah, H. H., & Al Zoubi, K. Y. (2019). P-expandable spaces. Italian Journal of Pure and Applied Mathematics, 41 (3), 497–507.
8. De Arruda Saraiva, L. E. (2011). Generalized quotient topologies. Acta Mathematica Hungarica, 132, 168–173.

9. Demir, I., & Ozbakir, O. B. (2013). β-expandable spaces. Filomat, 27 (6), 971–976.
10. Krajewski, L. L. (1971). On expanding locally finite collections. Canadian Journal of Mathematics, 23 (1), 58–68.
11. Levine, N. (1963). Semi-open sets and semi-continuity in topological spaces. The American Mathematical Monthly, 70 (1), 36–41.
12. 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.
13. Njastad, O. (1965). On some classes of nearly open sets. Pacific Journal of Mathematics, 15 (3), 961–970.
14. 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.
15. Ray, A. D., & Bhowmick, R. (2014). μ-paracompact and μ-paracompact generalized topological spaces. Hacettepe Journal of Mathematics and Statistics, 45 (2), 447–453.
16. Sarsak, M. S. (2013). On μ-compact sets in μ-spaces. Questions and Answers in General Topology, 31, 49–57.
17. Zuhier, A., & Jawarneh, I. (2022). μ-countably compactness and μH-countably compactness. Communications of the Korean Mathematical Society, 37 (1), 269–277.