Nodecness of Soft Generalized Topological Spaces

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-149
Published: Sep 2, 2024
Cite as:
Mesfer H. Alqahtani, Ohud F. Alghamdi, Zanyar A. Ameen, Nodecness of Soft Generalized Topological Spaces, Int. J. Anal. Appl., 22 (2024), 149.

Main Article Content

Mesfer H. Alqahtani, Ohud F. Alghamdi, Zanyar A. Ameen

Abstract

In this work, we define a new class of soft generalized topological spaces, namely strongly soft nodec, with the use of strongly soft nowhere dense sets. Then, we study the basic properties of these spaces and show that if the product of two soft generalized topological spaces is a strongly soft nodec space, then each one is a strongly soft nodec space. Then, we extend these notions to T0-strongly soft nodec generalized topological spaces by using the soft quotient functions and discussing their main properties. We also show the inverse of a surjective soft quotient function preserves the soft closure and soft interior of a soft subset of a codomain soft set in soft generalized topological space. Further, we use soft quasi-homeomorphism and soft quotient functions to make comparisons and connections between these spaces with the support of appropriate counterexamples. Then, we successfully determine a condition under which the soft generalized topological space is a soft weak Baire space and hence a strongly soft second category.

Article Details

References

  1. A.M. Abd El-latif, M.H. Alqahtani, New Soft Operators Related to Supra Soft δi -Open Sets and Applications, AIMS Math. 9 (2024), 3076–3096. https://doi.org/10.3934/math.2024150.
  2. 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.
  3. S.A. Ghour, Soft ωb-Openness and Soft b-Lindelofness, Int. J. Fuzzy Logic Intell. Syst. 23 (2023), 181–191. https://doi.org/10.5391/ijfis.2023.23.2.181.
  4. S. Al Ghour, Z.A. Ameen, On Soft Submaximal Spaces, Heliyon 8 (2022), e10574. https://doi.org/10.1016/j.heliyon.2022.e10574.
  5. T.M. Al-shami, Z.A. Ameen, R. Abu-Gdairi, A. Mhemdi, On Primal Soft Topology, Mathematics 11 (2023), 2329. https://doi.org/10.3390/math11102329.
  6. 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.
  7. M.H. Alqahtani, Z.A. Ameen, Soft Nodec Spaces, AIMS Math. 9 (2024), 3289–3302. https://doi.org/10.3934/math.2024160.
  8. 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.
  9. Z. Ameen A., G. Al Samer, Extensions of Soft Topologies, Filomat 36 (2022), 5279–5287. https://doi.org/10.2298/fil2215279a.
  10. Z.A. Ameen, S. Al Ghour, Cluster Soft Sets and Cluster Soft Topologies, Comp. Appl. Math. 42 (2023), 37. https://doi.org/10.1007/s40314-023-02476-7.
  11. Z.A. Ameen, O.F. Alghamdi, B. Asaad, R.A. Mohammed, Methods of Generating Soft Topologies and Soft Separation Axioms, Eur. J. Pure Appl. Math. 17 (2024), 1168–1182. https://doi.org/10.29020/nybg.ejpam.v17i2.5161.
  12. Z.A. Ameen, M.H. Alqahtani, Baire Category Soft Sets and Their Symmetric Local Properties, Symmetry 15 (2023), 1810. https://doi.org/10.3390/sym15101810.
  13. Z.A. Ameen, M.H. Alqahtani, Congruence Representations via Soft Ideals in Soft Topological Spaces, Axioms 12 (2023), 1015. https://doi.org/10.3390/axioms12111015.
  14. 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.
  15. Z.A. Ameen, M.H. Alqahtani, O.F. Alghamdi, Lower Density Soft Operators and Density Soft Topologies, Heliyon 10 (2024), e35280. https://doi.org/10.1016/j.heliyon.2024.e35280.
  16. Z.A. Ameen, B.A. Asaad, T.M. Al-Shami, Soft Somewhat Continuous and Soft Somewhat Open Functions, TWMS J. Pure Appl. Math. 13 (2023), 792–806.
  17. B.A. Asaad, Results on Soft Extremally Disconnectedness of Soft Topological Spaces, J. Math. Comp. Sci. 17 (2017), 448–464. https://doi.org/10.22436/jmcs.017.04.02.
  18. B.A. Asaad, T.M. Al-shami, Z.A. Ameen, On Soft Somewhere Dense Open Functions and Soft Baire Spaces, Iraqi J. Sci. 64 (2023), 373–384. https://doi.org/10.24996/ijs.2023.64.1.35.
  19. A. Aygüno ˘glu, H. Aygün, Some Notes on Soft Topological Spaces, Neural Comp. Appl. 21 (2011), 113–119. https://doi.org/10.1007/s00521-011-0722-3.
  20. A.A. Azzam, Z.A. Ameen, T.M. Al-shami, M.E. El-Shafei, Generating Soft Topologies via Soft Set Operators, Symmetry 14 (2022), 914. https://doi.org/10.3390/sym14050914.
  21. S. Bayramov, C. Gunduz, A New Approach to Separability and Compactness in Soft Topological Spaces, TWMS J. Pure Appl. Math. 9 (2018), 82–93.
  22. A. Császár, Generalized Topology, Generized Continuity, Acta Math. Hung. 96 (2002), 351–357. https://doi.org/10.1023/a:1019713018007.
  23. S. Das, S. Samanta, Soft Metric, Ann. Fuzzy Math. Inf. 6 (2013), 77–94.
  24. A. Kharal, B. Ahmad, Mappings on Soft Classes, New Math. Nat. Comp. 7 (2011), 471–481.
  25. E. Korczak-Kubiak, A. Loranty, R.J. Pawlak, Baire Generalized Topological Spaces, Generalized Metric Spaces and Infinite Games, Acta Math. Hung. 140 (2013), 203–231. https://doi.org/10.1007/s10474-013-0304-1.
  26. F. Lin, Soft Connected Spaces and Soft Paracompact Spaces, Int. J. Math. Comp. Sci. 7 (2013), 277–283.
  27. 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.
  28. A. Mhemdi, The Category of Soft Topological Spaces and the T0-Reflection, J. Math. Comp. Sci. 22 (2020), 1–8. https://doi.org/10.22436/jmcs.022.01.01.
  29. D. Molodtsov, Soft Set Theory–First Results, Comp. Math. Appl. 37 (1999), 19–31. https://doi.org/10.1016/s0898-1221(99)00056-5.
  30. S. Nazmul, S. Samanta, Neighbourhood Properties of Soft Topological Spaces, Ann. Fuzzy Math. Inf. 6 (2013), 1–15.
  31. 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.
  32. 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.
  33. J. Thomas, S.J. Johna, On Soft Generalized Topological Spaces, J. New Results Sci. 3 (2014), 1–15.
  34. S. Vadakasi, V. Renukadevi, Properties of Nowhere Dense Sets in GTSs, Kyungpook Math. J. 57 (2017), 199–210. https://doi.org/10.5666/KMJ.2017.57.2.199.
  35. N. ie, Soft Points and the Structure of Soft Topological Spaces, Ann. Fuzzy Math. Inf. 10 (2015), 309–322.
  36. ˙I. Zorlutuna, M. Akdag, W. Min, S. Atmaca, Remarks on Soft Topological Spaces, Ann. Fuzzy Math. Inf. 3 (2012), 171–185.