Novel Approaches to Supra Soft Topological Structures via sd-Boundary and sd-Derived Operators

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DOI: https://doi.org/10.28924/2291-8639-24-2026-140
Published: Apr 30, 2026
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Diana Mahmoud, Salsabiela Rawashdeh, Jamal Oudetallah, Ala Amourah, Abdullah Alsoboh, Jamal Salah, Tala Sasa, Novel Approaches to Supra Soft Topological Structures via sd-Boundary and sd-Derived Operators, Int. J. Anal. Appl., 24 (2026), 140.

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Diana Mahmoud, Salsabiela Rawashdeh, Jamal Oudetallah, Ala Amourah, Abdullah Alsoboh, Jamal Salah, Tala Sasa

Abstract

In this paper, we introduce groundbreaking concepts of supra soft sd-boundary and sd-derived operators in the framework of supra soft topological spaces (SSTSs). These novel operators lead to the development of new categories of soft continuous maps, namely supra soft sd-boundary continuous, sd-derived continuous, and sd-frontier continuous maps. We establish comprehensive characterizations of these maps through various soft operators and investigate their intricate relationships. Furthermore, we introduce the revolutionary concept of supra soft sd-extremally disconnected spaces, which generalizes existing notions of disconnectedness in soft topological settings. The preservation properties of extreme disconnectedness of sd under different classes of soft maps are thoroughly examined. We also develop the theory of supra soft sd-resolvable spaces using sd-derived operators, revealing deep connections with sd-boundary properties. Our results are supported by rigorous mathematical proofs and illuminating counterexamples that demonstrate the independence of various concepts. This work opens new avenues for research in soft topology and provides powerful tools for analyzing the structure of supra soft topological spaces.

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References

  1. A.S. Mashhour, A.A. Allam, F.S. Mahmoud, F.H. Khedr, On Supratopological Spaces, Indian J. Pure Appl. Math. 14 (1983), 502–510.
  2. A.M. Kozae, M. Shokry, M. Zidan, Supra Topologies for Digital Plane, AASCIT Commun. 3 (2016), 1–10.
  3. M.E. El-Shafei, A.H. Zakari, T.M. Al-shami, Some Applications of Supra Preopen Sets, J. Math. 2020 (2020), 9634206. https://doi.org/10.1155/2020/9634206.
  4. T.M. Al-Shami, E.A. Abo-Tabl, B.A. Asaad, Investigation of Limit Points and Separation Axioms Using Supra $beta$-Open Sets, Mo. J. Math. Sci. 32 (2020), 171–187. https://doi.org/10.35834/2020/3202171.
  5. T.M. Al-shami, I. Alshammari, Rough Sets Models Inspired by Supra-Topology Structures, Artif. Intell. Rev. 56 (2022), 6855–6883. https://doi.org/10.1007/s10462-022-10346-7.
  6. D. Molodtsov, Soft Set Theory—First Results, Comput. Math. Appl. 37 (1999), 19–31. https://doi.org/10.1016/s0898-1221(99)00056-5.
  7. P. Maji, R. Biswas, A. Roy, Soft Set Theory, Comput. Math. Appl. 45 (2003), 555–562. https://doi.org/10.1016/s0898-1221(03)00016-6.
  8. N. Çağman, S. Enginoğlu, Soft Matrix Theory and Its Decision Making, Comput. Math. Appl. 59 (2010), 3308–3314. https://doi.org/10.1016/j.camwa.2010.03.015.
  9. F. Karaaslan, Soft Classes and Soft Rough Classes with Applications in Decision Making, Math. Probl. Eng. 2016 (2016), 1584528 https://doi.org/10.1155/2016/1584528.
  10. A. Abd El-Latif, Generalized Soft Rough Sets and Generated Soft Ideal Rough Topological Spaces, J. Intell. Fuzzy Syst. 34 (2018), 517–524. https://doi.org/10.3233/jifs-17610.
  11. S. Yuksel, T. Dizman, G. Yildizdan, U. Sert, Application of Soft Sets to Diagnose the Prostate Cancer Risk, J. Inequal. Appl. 2013 (2013), 229. https://doi.org/10.1186/1029-242x-2013-229.
  12. A. Kharal, B. Ahmad, Mappings on Soft Classes, New Math. Nat. Comput. 07 (2011), 471–481. https://doi.org/10.1142/s1793005711002025.
  13. Z.A. Ameen, M.H. Alqahtani, Some Classes of Soft Functions Defined by Soft Open Sets Modulo Soft Sets of the First Category, Mathematics 11 (2023), 4368. https://doi.org/10.3390/math11204368.
  14. I. Zorlutuna, H. Cakır, On Continuity of Soft Mappings, Appl. Math. Inf. Sci. 9 (2015), 403–409. https://doi.org/10.12785/amis/010147.
  15. Z.A. Ameen, A Non-Continuous Soft Mapping That Preserves Some Structural Soft Sets, J. Intell. Fuzzy Syst. 42 (2022), 5839–5845. https://doi.org/10.3233/jifs-212410.
  16. M. Shabir, M. Naz, On Soft Topological Spaces, Comput. Math. Appl. 61 (2011), 1786–1799. https://doi.org/10.1016/j.camwa.2011.02.006.
  17. N. Çağman, S. Karataş, S. Enginoglu, Soft Topology, Comput. Math. Appl. 62 (2011), 351–358. https://doi.org/10.1016/j.camwa.2011.05.016.
  18. A. Kandil, O.A.E. Tantawy, S.A. El-Sheikh, A.M. Abd El-latif, Soft Semi Separation Axioms and Some Types of Soft Functions, Ann. Fuzzy Math. Inform. 8 (2014), 305–318.
  19. B. Chen, Soft Semi-Open Sets and Related Properties in Soft Topological Spaces, Appl. Math. Inf. Sci. 7 (2013), 287–294. https://doi.org/10.12785/amis/070136.
  20. T.M. Al-shami, A. Mhemdi, R. Abu-Gdairi, A Novel Framework for Generalizations of Soft Open Sets and Its Applications via Soft Topologies, Mathematics 11 (2023), 840. https://doi.org/10.3390/math11040840.
  21. S.A. El-Sheikh, A.M. El-Latif, Characterization of b-Open Soft Sets in Soft Topological Spaces, J. New Theory 2 (2015), 8–18.
  22. M. Akdag, A. Ozkan, Soft b-Open Sets and Soft b-Continuous Functions, Math. Sci. 8 (2014), 124. https://doi.org/10.1007/s40096-014-0124-7.
  23. T.M. Al-shami, Soft Somewhere Dense Sets on Soft Topological Spaces, Commun. Korean Math. Soc. 33 (2018), 1341–1356. https://doi.org/10.4134/CKMS.c170378.
  24. Z.A. Ameen, R. Abu-Gdairi, T.M. Al-Shami, B.A. Asaad, M. Arar, Further Properties of Soft Somewhere Dense Continuous Functions and Soft Baire Spaces, J. Math. Comput. Sci. 32 (2023), 54–63. https://doi.org/10.22436/jmcs.032.01.05.
  25. Ain Shams University, Cairo, Egypt, S.A. El-Sheikh, A.M. Abd El-latif, Decompositions of Some Types of Supra Soft Sets and Soft Continuity, Int. J. Math. Trends Technol. 9 (2014), 37–56. https://doi.org/10.14445/22315373/ijmtt-v9p504.
  26. A.M. Abd El-latif, S. Karataş, Supra b-Open Soft Sets and Supra b-Soft Continuity on Soft Topological Spaces, J. Math. Comput. Appl. Res. 5 (2015), 1–18.
  27. A.M. Abd El-latif, M.H. Alqahtani, New Soft Operators Related to Supra Soft $ delta_i$-Open Sets and Applications, AIMS Math. 9 (2024), 3076–3096. https://doi.org/10.3934/math.2024150.
  28. A.M. Abd El-latif, Novel Types of Supra Soft Operators via Supra Soft Sd-Sets and Applications, AIMS Math. 9 (2024), 6586–6602. https://doi.org/10.3934/math.2024321.
  29. A.M. Abd El-latif, M.H. Alqahtani, F.A. Gharib, Strictly Wider Class of Soft Sets via Supra Soft $delta$-Closure Operator, Int. J. Anal. Appl. 22 (2024), 47. https://doi.org/10.28924/2291-8639-22-2024-47.
  30. A.M. Abd El-latif, Decomposition of Supra Soft Locally Closed Sets and Supra SLC-Continuity, Int. J. Nonlinear Anal. Appl. 9 (2018), 13–25. https://doi.org/10.22075/ijnaa.2018.12727.1651.
  31. W. Rong, F. Lin, Soft Connected Spaces and Soft Paracompact Spaces, Int. J. Appl. Math. Stat. 51 (2013), 667–681.
  32. H.L. Yang, On Soft Continuous Mappings and Soft Connectedness of Soft Topological Spaces, Hacet. J. Math. Stat. 6 (2015), 385–398. https://doi.org/10.15672/HJMS.2015459876.
  33. S. Hussain, A Note on Soft Connectedness, J. Egypt. Math. Soc. 23 (2015), 6–11. https://doi.org/10.1016/j.joems.2014.02.003.
  34. S.S. Thakur, A.S. Rajput, Connectedness Between Soft Sets, New Math. Nat. Comput. 14 (2018), 53–71. https://doi.org/10.1142/s1793005718500059.
  35. J. Oudetallah, W. Alharbi, R. Alharbi, A. Amourah, A. Alsoboh, F. Al-Sharqi, T. Sasa, Neutrosophic Tri-metric Space and Its Topological Properties, Neutrosophic Sets Syst. 95 (2026), 75–98.
  36. F. Al-Sharqi, Jamal Oudetallah, Wedad Alharbi, Rehab Alharbi, Ala Amourah, et al., Neutrosophic N-Metric Spaces: Generalized Fixed Point Theory and Topological Properties, Gulf J. Math. 21 (2025), 288–300. https://doi.org/10.56947/gjom.v21i2.3631.
  37. E. Hussein, A.A.R. Malkawi, A. Amourah, A. Alsoboh, A. Al Kasbi, et al., Foundations of Neutrosophic Mr-Metric Spaces with Applications to Homotopy, Fixed Points, and Complex Networks, Eur. J. Pure Appl. Math. 18 (2025), 7142. https://doi.org/10.29020/nybg.ejpam.v18i4.7142.
  38. A. Alsoboh, J. Oudetallah, A. Amourah, R. Al-Naimi, M. Al Hatmi, et al., Bi-Metric Structures and Their Applications in Bitopological Contexts, Eur. J. Pure Appl. Math. 18 (2025), 6526. https://doi.org/10.29020/nybg.ejpam.v18i4.6526.
  39. A.M. Jaradat, Y. Al-Qudah, A. Alsoboh, F. Al-Sharqi, A.A. Al-Maqbali, A New Approach of Possibility Single-Valued Neutrosophic Set and Its Application in Decision-Making Environment, Int. J. Anal. Appl. 23 (2025), 213. https://doi.org/10.28924/2291-8639-23-2025-213.
  40. M. Shatnawi, J. Oudetallah, A. Bataiha, A. Amourah, A. Alsoboh, et al., G-Compact Spaces Characterized by the Intersection of Countable Neighborhoods, Eur. J. Pure Appl. Math. 18 (2025), 6067. https://doi.org/10.29020/nybg.ejpam.v18i3.6067.
  41. S. Hussain, Binary Soft Connected Spaces and an Application of Binary Soft Sets in Decision Making Problem, Fuzzy Inf. Eng. 11 (2019), 506–521. https://doi.org/10.1080/16168658.2020.1773600.
  42. A. Kandil, O.A.E. Tantawy, S.A. El-Sheikh, A.M. Abd El-latif, Soft Connectedness via Soft Ideals, J. New Results Sci. 4 (2014), 90–108.
  43. A. Kandil, O.A.E. Tantawy, S.A. El-Sheikh, A.M. Abd El-latif, Soft Ideal Theory Soft Local Function and Generated Soft Topological Spaces, Appl. Math. Inf. Sci. 8 (2014), 1595–1603. https://doi.org/10.12785/amis/080413.
  44. A. Kandil, O.A.E. Tantawy, S.A. El-Sheikh, A.M. Abd El-latif, Supra Generalized Closed Soft Sets with Respect to an Soft Ideal in Supra Soft Topological Spaces, Appl. Math. Inf. Sci. 8 (2014), 1731–1740. https://doi.org/10.12785/amis/080430.
  45. M.E. El-Shafei, T.M. Al-Shami, Some Operators of a Soft Set and Soft Connected Spaces Using Soft Somewhere Dense Sets, J. Interdiscip. Math. 24 (2021), 1471–1495. https://doi.org/10.1080/09720502.2020.1842348.
  46. A.M.A. El-Latif, Supra Soft b-Connectedness I: Supra Soft b-Irresoluteness and Separateness, Creat. Math. Inform. 25 (2016), 127–134. https://doi.org/10.37193/cmi.2016.02.02.
  47. A.M.A. Abd El-Latif, Supra Soft b-Connectedness II: Some Types of Supra Soft B-Connectednes, Creat. Math. Inform. 26 (2017), 1–8. https://doi.org/10.37193/cmi.2017.01.01.
  48. A.M.A. El-latif, M.H. Alqahtani, Novel Categories of Supra Soft Continuous Maps via New Soft Operators, AIMS Math. 9 (2024), 7449–7470. https://doi.org/10.3934/math.2024361.
  49. J. Oudetallah, Nearly Metacompact in Bitopological Space, Int. J. Open Probl. Comput. Math. 15 (2022), 6–11.
  50. J. Oudetallah, M. AL-Hawari, Other Generalization of Pairwise Expandable Spaces, Int. Math. Forum 16 (2021), 1–9. https://doi.org/10.12988/imf.2021.912116.
  51. J.A. Oudetallah, h-Convexity in Metric Linear Spaces, Int. J. Sci. Appl. Inf. Technol. 8 (2019), 51–58. https://doi.org/10.30534/ijsait/2019/07862019.
  52. J. Oudetallah, R. Alharbi, I.M. Batiha, On r-Compactness in Topological and Bitopological Spaces, Axioms 12 (2023), 210. https://doi.org/10.3390/axioms12020210.
  53. J. Oudetallah, M.M. Rousan, I.M. Batiha, On D-Metacompactness in Topological Spaces, J. Appl. Math. Inform. 39 (2021), 919–926. https://doi.org/10.14317/jami.2021.919.
  54. J. Oudetallah, Novel Results on Nigh Lindelöfness in Topological Spaces, Int. J. Anal. Appl. 22 (2024), 153. https://doi.org/10.28924/2291-8639-22-2024-153.