Some Separation Axioms via Soft Somewhat Open Sets

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-205
Published: Nov 11, 2024
Cite as:
Wafa Alqurashi, Some Separation Axioms via Soft Somewhat Open Sets, Int. J. Anal. Appl., 22 (2024), 205.

Main Article Content

Wafa Alqurashi

Abstract

It is commonly known that some topological spaces include structures that may be used to expand abstract notions. somewhat open sets and soft sets is such sort of structures. We obtain several properties and symmetry of the soft somewhat-R0 spaces and soft somewhat-R1 spaces obtained. Furthermore, we present new theorems and results and investigated relation between this concepts and the other structures.

Article Details

References

  1. D. Molodtsov, Soft Set Theory–First Results, Comp. Math. Appl. 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5.
  2. P.K. Maji, R. Biswas, A.R. Roy, Soft Set Theory, Comp. Math. Appl. 45 (2003), 555–562. https://doi.org/10.1016/S0898-1221(03)00016-6.
  3. T.M. Al-Shami, M.E. El-Shafei, T-Soft Equality Relation, Turk. J. Math. 44 (2020), 1427–1441. https://doi.org/10.3906/mat-2005-117.
  4. N. Cagman, S. Karatas, S. Enginoglu, Soft Topology, Comp. Math. Appl. 62 (2011), 351–358. https://doi.org/10.1016/j.camwa.2011.05.016.
  5. M. Shabir, M. Naz, On Soft Topological Spaces, Comp. Math. Appl. 61 (2011), 1786–1799. https://doi.org/10.1016/j.camwa.2011.02.006.
  6. S.K. Nazmul, S.K. Samanta, Neighbourhood Properties of Soft Topological Spaces, Ann. Fuzzy Math. Inf. 6 (2013), 1–15.
  7. J. Mahanta, P.K. Das, On Soft Topological Space via Semiopen and Semiclosed Soft Sets, Kyungpook Math. J. 54 (2014), 221–236. https://doi.org/10.5666/KMJ.2014.54.2.221.
  8. Y. Yumak, A.K. Kaymakci, Soft β-Open Sets and their Applications, J. New Theory 4 (2015), 80–89.
  9. T. Al-Shami, I. Alshammari, B. Asaad, Soft Maps via Soft Somewhere Dense Sets, Filomat 34 (2020), 3429–3440. https://doi.org/10.2298/FIL2010429A.
  10. M. E. El-Shafei, M. Abo-Elhamayel and T. M. Al-shami, Partial soft separation axioms and soft compact spaces, Filomat 32(13) (2018), 4755–4771. https://doi.org/10.2298/FIL1813755E.
  11. A. Al-Omari, W. Alqurashi, Hyperconnectedness and Resolvability of Soft Ideal Topological Spaces, Mathematics 11 (2023), 4697. https://doi.org/10.3390/math11224697.
  12. A. Al-Omari, Soft Topology in Ideal Topological Spaces, Hacettepe J. Math. Stat. 48 (2018), 1277–1285. https://doi.org/10.15672/HJMS.2018.557.
  13. A. A. Allam, Ramadhan A. Mohammed, Tahir H. Ismail, A New Approach to Soft Belonging, Ann. Fuzzy Math. Inf. 13 (2017), 145–152. https://doi.org/10.30948/AFMI.2017.13.1.145.
  14. M.I. Ali, F. Feng, X. Liu, W.K. Min, M. Shabir, On Some New Operations in Soft Set Theory, Comp. Math. Appl. 57 (2009), 1547–1553. https://doi.org/10.1016/j.camwa.2008.11.009.
  15. S. Bayramov, C.G. Aras, A New Approach to Separability and Compactness in Soft Topological Spaces, TWMS J. Pure Appl. Math. 9 (2018), 82–93.
  16. I. Zorlutuna, M. Akdag, W.K. Min, S. Atmaca, Remarks on Soft Topological Spaces, Ann. Fuzzy Math. Inf. 3 (2012), 171–185.
  17. Z.A. Ameen, B.A. Asaad, T.M. Al-shami, Soft Somewhat Continuous and Soft Somewhat Open Functions, TWMS J. Appl. Eng. Math. 13 (2023), 792–806.
  18. T.M. Al-shami, Soft Somewhat Open Sets: Soft Separation Axioms and Medical Application to Nutrition, Comp. Appl. Math. 41 (2022), 216. https://doi.org/10.1007/s40314-022-01919-x.
  19. B. Tanay, M.B. Kandemir, Topological Structure of Fuzzy Soft Sets, Comp. Math. Appl. 61 (2011), 2952–2957. https://doi.org/10.1016/j.camwa.2011.03.056.
  20. J.K. Syed, L.A. Aziz, Fuzzy Inventory Model without Shortages Using Signed Distance Method, Appl. Math. Inf. Scie. 1 (2007), 203–209.
  21. J. Xiao, M. Tong, Q. Fan, S. Xiao, Generalization of Belief and Plausibility Functions to Fuzzy Sets. Appl. Math. Inf. Sci. 6 (2012), 697–703.
  22. Z. Xiao, L. Chen, B. Zhong, S. Ye, Recognition for Soft Information Based on the Theory of Soft Sets, in: Proceedings of 2005 International Conference on Services Systems and Services Management, 2005, IEEE, Chongquing, China, 2005: pp. 1104–1106. https://doi.org/10.1109/ICSSSM.2005.1500166.
  23. D. Pei, D. Miao, From Soft Sets to Information Systems, in: 2005 IEEE International Conference on Granular Computing, IEEE, Beijing, China, 2005: pp. 617–621. https://doi.org/10.1109/GRC.2005.1547365.
  24. A. Al-Omari, W. Alqurashi, Connectedness of Soft-Ideal Topological Spaces, Symmetry 16 (2024), 143. https://doi.org/10.3390/sym16020143.
  25. S. Al Ghour, A. Al-Omari, T. Noiri, On Homogeneity and Homogeneity Components in Generalized Topological Spaces, Filomat 27 (2013), 1097–1105. https://doi.org/10.2298/FIL1306097A.