TY - JOUR T1 - On $\mu$-paracompact and $\mu$-expandable spaces TT - On $\mu$-paracompact and $\mu$-expandable spaces AU - Sarkar, Nırmal AU - Aman, Towhıd AU - Das, Ashoke PY - 2025 DA - October Y2 - 2025 DO - 10.33773/jum.1595789 JF - Journal of Universal Mathematics JO - JUM PB - Gökhan ÇUVALCIOĞLU WT - DergiPark SN - 2618-5660 SP - 85 EP - 92 VL - 8 IS - 2 LA - en AB - 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. KW - Generalized topology KW - $\mu$-paracompact KW - $\mu$-expandable KW - $\mu$-locally finite. N2 - 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. CR - Császár, Á. (1997). Generalized open sets. Acta Mathematica Hungarica, 75, 65–87. CR - Császár, Á. (2002). Generalized topology, generalized continuity. Acta Mathematica Hungarica, 96, 351– 357. CR - Arar, M. (2014). A note on spaces with a countable μ-base. Acta Mathematica Hungarica, 144, 494–498. CR - Arar, M. (2016). On countably μ-paracompact spaces. Acta Mathematica Hungarica, 149, 50–57. CR - 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. CR - Al-Zoubi, K. (2004). s-expandable spaces. Acta Mathematica Hungarica, 102 (3), 203–210. CR - Al-Jarrah, H. H., & Al Zoubi, K. Y. (2019). P-expandable spaces. Italian Journal of Pure and Applied Mathematics, 41 (3), 497–507. CR - De Arruda Saraiva, L. E. (2011). Generalized quotient topologies. Acta Mathematica Hungarica, 132, 168–173. CR - Demir, I., & Ozbakir, O. B. (2013). β-expandable spaces. Filomat, 27 (6), 971–976. CR - Krajewski, L. L. (1971). On expanding locally finite collections. Canadian Journal of Mathematics, 23 (1), 58–68. CR - Levine, N. (1963). Semi-open sets and semi-continuity in topological spaces. The American Mathematical Monthly, 70 (1), 36–41. CR - 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. CR - Njastad, O. (1965). On some classes of nearly open sets. Pacific Journal of Mathematics, 15 (3), 961–970. CR - 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. CR - Ray, A. D., & Bhowmick, R. (2014). μ-paracompact and μ-paracompact generalized topological spaces. Hacettepe Journal of Mathematics and Statistics, 45 (2), 447–453. CR - Sarsak, M. S. (2013). On μ-compact sets in μ-spaces. Questions and Answers in General Topology, 31, 49–57. CR - Zuhier, A., & Jawarneh, I. (2022). μ-countably compactness and μH-countably compactness. Communications of the Korean Mathematical Society, 37 (1), 269–277. UR - https://doi.org/10.33773/jum.1595789 L1 - https://dergipark.org.tr/en/download/article-file/4414390 ER -