Abstract
This paper introduces a new topological class called soft S-paracompact spaces. These spaces generalize the concept of soft paracompact spaces. A soft topological space is considered soft S-paracompact if every soft open cover has a locally finite soft semi-open refinement. We explore the key properties of soft S-paracompact spaces and investigate their relationships with other well-established soft topological spaces. We depict an application of soft S-paracompactness in the decision-making problem.
Full text article
References
L. A. Zadeh, “Fuzzy sets,” Information and control, vol. 8, no. 3, pp. 338–353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X.
D. Molodtsov, “Soft set theory—first results,” Computers & mathematics with applications, vol. 37, no. 4-5, pp. 19–31, 1999. https://www.sciencedirect.com/science/article/pii/S0898122199000565.
P. K. Maji, R. Biswas, and A. R. Roy, “Soft set theory,” Computers & mathematics with applications, vol. 45, no. 4-5, pp. 555–562, 2003. https://www.sciencedirect.com/science/article/pii/S0898122103000166.
M. Shabir and M. Naz, “On soft topological spaces,” Computers & Mathematics with Applications, vol. 61, no. 7, pp. 1786–1799, 2011. https://www.sciencedirect.com/science/article/pii/S0898122111000927.
N. C¸ a˘gman, S. Karata¸s, and S. Enginoglu, “Soft topology,” Computers & Mathematics with Applications, vol. 62, no. 1, pp. 351–358, 2011. https://www.sciencedirect.com/science/article/pii/S0898122111004044.
S. Engino˘glu, N. C¸ a˘gman, S. Karata¸s, and T. Aydın, “On soft topology,” El-Cezeri, vol. 2, no. 3, pp. 23–38, 2015. https://dergipark.org.tr/tr/download/article-file/56984.
N. Levine, “Semi-open sets and semi-continuity in topological spaces,” The American mathematical monthly, vol. 70, no. 1, pp. 36–41, 1963. https://www.jstor.org/stable/2312781.
K. Y. Al-Zoubi, “S-paracompact spaces,” Acta Mathematica Hungarica, vol. 110, no. 1-2 pp. 165–174, 2006. Available at: https://doi.org/10.1007/s10474-006-0001-4.
D. Jankovi´c, “A note on mappings of extremally disconnected spaces,” Acta Mathematica Hungarica, vol. 46, no. 1-2, pp. 83–92, 1985. Available at: https://link.springer.com/article/10.1007/BF01961010.
T. Thompson, “s-closed spaces,” Proceedings of the American Mathematical Society, vol. 60, no. 1, pp. 335–338, 1976. Available at: https://www.jstor.org/stable/2041169.
K. Dlaska, N. Ergun, and M. Ganster, “Countably s-closed spaces,” Mathematica Slovaca, vol. 44, no. 3, pp. 337–348, 1994. Available at: https://dml.cz/handle/10338.dmlcz/136612.
N. Ergun, “On nearly paracompact spaces,” Istanbul University Science Faculty the Journal of Mathematics Physics and Astronomy, vol. 45, pp. 65–87, 1980. https://dergipark.org.tr/tr/download/article-file/100388.
T. Baiju and S. J. John, “Mappings and covering properties in l-topological spaces,” Hacettepe journal of Mathematics and Statistics, vol. 39, no. 1, pp. 55–65, 2010. https://www.researchgate.net/profile/Sunil-John-2/publication/264962813.
B. Chen, “Soft semi-open sets and related properties in soft topological spaces,” Applied Mathematics & Information Sciences, vol. 7, no. 1, pp. 287–294, 2013. Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss1/36/.
F. Lin, “Soft connected spaces and soft paracompact spaces,” International Journal of Mathematical Science and Engineering, vol. 7, no. 2, pp. 1–7, 2013. https://www.researchgate.net/publication/292087439.
S. Hussain, “Properties of soft semi-open and soft semi-closed sets,” arXiv preprint, vol. arXiv:1409.3459, 2014. Available at: https://arxiv.org/abs/1409.3459.
S. Y¨uksel, N. Tozlu, and Z. G. Erg¨ul, “Soft regular generalized closed sets in soft topological spaces,” International Journal of Mathematical Analysis, vol. 8, no. 17-20, pp. 957-964, 2014. Available at: https://www.m-hikari.com/ijma/ijma-2014/ijma-5-8-2014/guzelergulIJMA5-8-2014.pdf.
B. Debnath, “A note on soft nearly compact and soft nearly paracompactness in soft topological spaces,” Int. J. Innov. Res. Sci. Eng. Technol, vol. 6, no. 8, pp. 15906–15914, 2017. https://www.ijirset.com/upload/2017/august/60_IJIRSET_Finnal_Paper_.pdf.
I. Zorlutuna, M. Akdag, W. Min, and S. Atmaca, “Remarks on soft topological spaces,” Annals of fuzzy Mathematics and Informatics, vol. 3, no. 2, pp. 171–185, 2012. https://www.researchgate.net/publication/296702749.
A. A. Rawshdeh, H. H. Al-Jarrah, and T. M. Al-Shami, “Soft expandable spaces,” Filomat, vol. 37, no. 9, pp. 2845–2858, 2023. https://www.pmf.ni.ac.rs/filomat-content/2023/37-9/37-9-16-18401.pdf.
I. Arockiarani and A. A. Lancy, “Generalized soft gβ-closed sets and soft gsβ-closed sets in soft topological spaces,” International Journal of Mathematical Archive, vol. 4, no. 2, pp. 1–7, 2013. https://scispace.com/papers/generalized-soft-gb-closed-sets-and-soft-gsb-closed-sets-in-3mrc69vwuk.
M. Akdag and A. Ozkan, “Soft α-open sets and soft α-continuous functions,” in Abstract and Applied Analysis, vol. 2014, p. 891341, Wiley Online Library, 2014. https://www.researchgate.net/publication/296774537.
B. A. Asaad, “Results on soft extremally disconnectedness of soft topological spaces,” J. Math. Comput. Sci, vol. 17, no. 4, pp. 448–464, 2017. https://www.researchgate.net/publication/319345341.
N. Demirta¸s and O. Dalkılı¸c, “Decompositions of softalpha-continuity and soft a-continuity,” Journal of New Theory, no. 31, pp. 86–94, 2020. https://dergipark.org.tr/en/pub/jnt/issue/55563/761266.
K. Kannan, “Soft generalized closed sets in soft topological spaces,” Journal of theoretical and applied information technology, vol. 37, no. 1, pp. 17–21, 2012. https://www.jatit.org/volumes/Vol37No1/2Vol37No1.pdf.
T. M. Al-shami, L. D. Koˇcinac, and B. A. Asaad, “Sum of soft topological spaces,” Mathematics, vol. 8, no. 6, p. 990, 2020. https://www.mdpi.com/2227-7390/8/6/990.
M. Milan, “Soft topological space and topology on the cartesian product,” Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 4, pp. 1091–1100, 2016. https://dergipark.org.tr/tr/download/article-file/644879.
S. S. Pai and T. Baiju, “Mappings and products in soft l-topological spaces,” J. Math. Comput. Sci., vol. 11, no. 4, pp. 4943–4959, 2021. https://scik.org/index.php/jmcs/article/viewFile/5506/2948.
J. Mahanta and P. K. Das, “On soft topological space via semiopen and semiclosed soft sets,” arXiv preprint arXiv:1203.4133, 2012. https://www.researchgate.net/publication/221711073.
P. K. Maji, A. R. Roy, and R. Biswas, “An application of soft sets in a decision making problem,” Computers & mathematics with applications, vol. 44, no. 8-9, pp. 1077–1083, 2002. https://www.sciencedirect.com/science/article/pii/S089812210200216X.
R. Mareay, M. Ali, and T. Medhat, “Soft sets and soft topological spaces via its applications,” Kafrelsheikh Journal of Information Sciences, vol. 3, no. 1, pp. 1–7, 2022. https://kjis.journals.ekb.eg/article_246103.html.
M. Atef, S. Nada, and A. Nawar, “Covering soft rough sets and its topological properties with application,” Soft Computing, vol. 27, no. 8, pp. 4451–4461, 2023. https://link.springer.com/article/10.1007/s00500-023-07812-x.
R. Sanjitha and B. THANKACHAN, “Aggregation operators on multiple sets and its application in decision-making problems.,” Global & Stochastic Analysis, vol. 11, no. 1, 2024. https://www.researchgate.net/publication/378713499.
Z. Pawlak, Rough sets: Theoretical aspects of reasoning about data, vol. 9. Springer Science & Business Media, 2012. https://link.springer.com/book/10.1007/978-94-011-3534-4.
T. Y. Lin et al., “Granular computing on binary relations ii: Rough set representations and belief functions,” Rough sets in knowledge discovery, vol. 1, pp. 122–140, 1998. https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=35bb5c1b87299a0e01db021bec501a90a01693ab.
Y. Yao, “Relational interpretations of neighborhood operators and rough set approximation operators,” Information sciences, vol. 111, no. 1-4, pp. 239–259, 1998. https://doi.org/10.1016/S0020-0255(98)10006-3.
Authors
Copyright (c) 2025 Journal of the Indonesian Mathematical Society
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Article Details
