New results on soft generalized topological spaces

Volume 32, Issue 1, pp 43--53 http://dx.doi.org/10.22436/jmcs.032.01.04

Publication Date: July 11, 2023 Submission Date: January 30, 2023 Revision Date: March 02, 2023 Accteptance Date: May 10, 2023

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 344 Downloads
• 1075 Views

Authors

J. Al-Mufarrij - Department of Mathematics, Women section, King Saud University, Riyadh 12372, KSA. S. Saleh - Department of Computer Science, Cihan University-Erbil, Erbil, Iraq. - Department of Mathematics, Hodeidah University, Hodeidah, Yemen.

Abstract

This work aims to introduce and discuss two new classes of separation properties namely, soft generalized \(R_0\) and \(R_1\) in a soft generalized topological space defined on an initial universe set, by using the notions of soft \(g\)-open sets and soft \(g\)-closure operator. We investigate some of their properties and characterizations. We further, investigate the relationships between different generalized structures of soft topology, providing some illustrative examples and results. Additionally, we present connections between these separation properties and those in some generated topologies. Furthermore, we show that being \({SGR}_i\), \(i=0,1\) are soft generalized topological properties.

Share and Cite

Keywords

• Soft sets
• soft \(g\)-open sets
• soft generalized topology
• \(Sg\)-closure
• \(SG\)-kernel
• soft generalized \(R_0\) and \(R_1\) spaces

MSC

•  54A05
•  54A40
•  54D15

References

• [1] H. Aktas¸, N. C¸ a˘gman, Soft sets and soft groups, Inform. Sci., 177 (2007), 2726–2735
  • View Article
  • MathSciNet
  • Google Scholar


• [2] A. Al-Omari, T. Noiri, A unified theory of contra-(, )-continuous functions in generalized topological spaces, Acta Math. Hungar., 135 (2012), 31–41
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] A. Al-Omari, Soft topology in ideal topological spaces, Hacet. J. Math. Stat., 48 (2019), 1277–1285
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] H. S. Al-Saadi, H. Ayg¨ un, A. Al-Omari, Some notes on soft hyperconnected spaces, J. Anal., 28 (2020), 351–362
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] T. M. Al-Shami, New Structure: Infra Soft Topological Spaces, Math. Probl. Eng., 2021 (2021), 12 Pages
  • View Article
  • Google Scholar


• [6] T. M. Al-Shami, Partial belong relation on soft separation axioms, two birds with one stone, Soft Comput., 24 (2020), 5377–5387
  • View Article
  • Google Scholar
  • MATH


• [7] N. C¸ a˘gman, S. Engino˘ glu, Soft set theory and uni-int decision making, European J. Oper. Res., 207 (2010), 848–855
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] N. C¸ a˘gman, S. Karatas¸, S. Enginoglu, Soft topology, Comput. Math. Appl., 62 (2011), 351–358
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] B. Chen, Soft semi-open sets and related properties in soft topological spaces, Appl. Math. Inf. Sci., 7 (2013), 287–294
  • View Article
  • MathSciNet
  • Google Scholar


• [10] A´ . Csa´sza´r, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), 351–357
  • View Article
  • MathSciNet
  • Google Scholar


• [11] S. Das, S. K. Samanta, Soft Matric, Annals Fuzzy Math. Info., 6 (2013), 77–94
  • View Article


• [12] S. A. El-Sheikh, A. M. Abd El-Latif, Decompositions of some types of supra soft sets and soft continuity, Int. J. Math. Trends Tech., 9 (2014), 37–56
  • View Article
  • Google Scholar


• [13] F. Feng, Y. B. Jun, X. Zhao, Soft semirings, Comput. Math. Appl., 56 (2008), 2621–2628
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] D. N. Georgiou, A. C. Megaritis, Soft set theory and topology, Appl. Gen. Topol., 15 (2014), 93–109
  • View Article
  • MathSciNet
  • Google Scholar


• [15] O. G¨oc¸ ¨ ur, A. Kopuzlu, Some new properties on soft separation axioms, Ann. Fuzzy Math. Inform., 9 (2015), 421–429
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] Y. B. Jun, C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci., 178 (2008), 2466–2475
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [17] A. Kharal, B. Ahmad, Mappings on soft classes, New Math. Nat. Comput., 7 (2011), 471–481
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] P. K. Maji, R. Biswas, R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555–562
  • View Article
  • MathSciNet
  • Google Scholar


• [19] P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002), 1077–1083
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] W. K. Min, A note on soft topological spaces, Comput. Math. Appl., 62 (2011), 3524–3528
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [21] D. Molodtsov, Soft set theory—first results, Comput. Math. Appl., 37 (1999), 19–31
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [22] B. Roy, On generalized R0 and R1 spaces, Acta Math. Hungar., 127 (2010), 291–300
  • View Article
  • Google Scholar


• [23] S. Saleh, On some new properties in soft topological spaces, Ann. Fuzzy Math. Inform., 17 (2019), 303–312
  • View Article


• [24] S. Saleh, K. Hur, On some lower soft separation axioms, Ann. Fuzzy Math. Inform., 19 (2020), 61–72
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [25] M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61 (2011), 1786–1799
  • View Article
  • MathSciNet
  • Google Scholar


• [26] O. Tantawy, S. A. El-Sheikh, S. Hamde, Separation axioms on soft topological spaces, Ann. Fuzzy Math. Inform., 11 (2016), 511–525
  • View Article
  • MATH


• [27] J. Thomas, S. J. John, On soft generalized topological spaces, J. New results Sci., 3 (2014), 1–15
  • View Article
  • Google Scholar


• [28] J. Thomas, J. John, On soft -compact soft generalized topological spaces, J. Uncertain. Math. Sci., 2014 (2014), 1–9
  • View Article
  • Google Scholar


• [29] J. Thomas, J. John, Soft generalized separation axioms in soft generalized topological spaces, Int. J. Sci. Eng. Res., 6 (2015), 969–974
  • View Article
  • Google Scholar


• [30] ˙I. Zorlutuna, M. Akdag, W. K. Min, S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform., 3 (2012), 171–185
  • View Article
  • Google Scholar
  • MATH