Soft functions via soft semi \(\omega \)-open sets

Volume 30, Issue 2, pp 133--146 https://doi.org/10.22436/jmcs.030.02.05

Publication Date: December 22, 2022 Submission Date: September 14, 2022 Revision Date: October 05, 2022 Accteptance Date: October 27, 2022

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)

• 416 Downloads
• 1035 Views

Authors

S. Al Ghour - Department of Mathematics and Statistics, Jordan University of Science and Technology, IRBID, Jordan.

Abstract

In this paper, we introduce the concepts of soft semi \( \omega \)-continuous, soft \(\omega \)-irresolute, and soft semi \(\omega \) -irresolute functions by using soft semi \(\omega \)-open sets. We characterize them and discuss their main properties with the help of examples. We investigate under what conditions the restriction of soft semi \( \omega \)-continuous, soft \(\omega \)-irresolute, and soft semi \(\omega \) -irresolute functions are respectively soft semi \(\omega \)-continuous, soft \( \omega \)-irresolute, and soft semi \(\omega \)-irresolute. Also, we investigate under what conditions the composition of two soft semi \(\omega \) -continuous, soft \(\omega \)-irresolute, and soft semi \(\omega \)-irresolute functions are respectively soft semi \(\omega \)-continuous, soft \(\omega \) -irresolute, and soft semi \(\omega \)-irresolute. In addition to these, we examine the connection between the new classes of soft functions and their corresponding general topological concepts.

Share and Cite

Keywords

• Soft semi continuous functions
• soft \(\omega \)-continuous functions
• semi \(\omega \)-continuous
• \(\omega \)-irresolute
• semi \(\omega \)-irresolute functions
• soft induced topological spaces

MSC

•  54C08
•  54C10
•  54B10

References

• [1] M. Akdag, A. Ozkan, Soft -open sets and soft -continuous functions, Abstr. Appl. Anal., 2014 (2014), 7 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [2] S. Al Ghour, Soft semi !-open sets, Mathematics, 9 (2021), 13 pages
  • View Article
  • Google Scholar


• [3] S. Al Ghour, Strong form of soft semi-open sets in soft topological spaces, Int. J. Fuzzy Logic Intel. Syst., 21 (2021), 159–168
  • View Article
  • Google Scholar


• [4] S. Al Ghour, Soft !-continuity and soft !s-continuity in soft topological spacesSoft !-continuity and soft !s-continuity in soft topological spaces, Int. J. Fuzzy Logic Intel. Syst., 22 (2022), 183–192
  • View Article
  • Google Scholar


• [5] S. Al Ghour, A. Bin-Saadon, On some generated soft topological spaces and soft homogeneity, Heliyon, 5 (2019), 11 pages
  • View Article
  • Google Scholar


• [6] S. Al Ghour, W. Hamed, On two classes of soft sets in soft topological spaces, Symmetry, 12 (2020), 14 pages
  • View Article
  • Google Scholar


• [7] T. M. Al-shami, Defining and investigating new soft ordered maps by using soft semi open sets, Acta Univ. Sapientiae Math., 13 (2021), 145–163
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] T. M. Al-shami, Improvement of the approximations and accuracy measure of a rough set using somewhere dense sets, Soft Comput., 25 (2021), 14449–14460
  • View Article
  • Google Scholar
  • MATH


• [9] T. M. Al-shami, B. A. Asaad, E. A. Abo-Tabl, Separation axioms and fixed points using total belong and total non-belong relations with respect to soft -open sets, J. Interdiscip. Math., 24 (2021), 1053–1077
  • View Article
  • Google Scholar


• [10] T. M. Al-shami, L. D. Kocinac, Almost soft Menger and weakly soft Menger spaces, Appl. Comput. Math., 21 (2022), 35–51
  • View Article
  • Google Scholar
  • MATH


• [11] T. M. Al-shami, A. Mhemdi, R. Abu-Gdairi, M. E. El-Shafei, Compactness and connectedness via the class of soft somewhat open sets, AIMS Math., 8 (2023), 815–840
  • View Article
  • MathSciNet
  • Google Scholar


• [12] T. M. Al-shami, A. Mhemdi, A. A. Rawshdeh, H. H. Al-Jarrah, Soft version of compact and lindel¨of spaces using soft somewhere dense sets, AIMS Math., 6 (2021), 8064–8077
  • View Article
  • Google Scholar


• [13] K. Al-Zoubi, Semi !-continuous functions, Abhath Al-Yarmouk, 12 (2003), 119–131
  • View Article
  • Google Scholar


• [14] Z. A. Ameen, A non-continuous soft mapping that preserves some structural soft sets, Journal of Intelligent and Fuzzy Systems, 42 (2022), 5839–5845
  • View Article
  • Google Scholar


• [15] Z. A. Ameen, T. M. Al-shami, A. Mhemdi, M. E. El-Shafei, The role of soft -topological operators in characterizing various soft separation axioms, J. Math., 2022 (2022), 7 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [16] A. A. Azzam, Z. A. Ameen, T. M. Al-shami, M. E. El-Shafei, Generating Soft Topologies via Soft Set Operators, Symmetry, 14 (2022), 9 pages
  • View Article
  • Google Scholar


• [17] S. G. Crossley, S. K. Hildebrand, Semi-topological properties, Fund. Math., 74 (1972), 233–254
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] S. Das, S. K. Samanta, Soft Metric, Ann. Fuzzy Math. Inform., 6 (2013), 77–94
  • View Article
  • Google Scholar


• [19] H. Z. Hdeib, !-closed mappings, Rev. Colombiana Mat., 16 (1982), 65–78
  • View Article
  • Google Scholar


• [20] H. Z. Hdeib, !-continuous functions, Dirasat, 16 (1989), 136–142
  • View Article
  • Google Scholar


• [21] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36–41
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [22] J. Mahanta, P. K. Das, On soft topological space via semiopen and semiclosed soft sets, Kyungpook Math. J., 54 (2014), 221–236
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


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


• [24] S. Y. Musa, B. A. Asaad, Connectedness on bipolar hypersoft topological spaces, J. Intel. Fuzzy Syst., 43 (2022), 4095– 4105
  • View Article
  • Google Scholar


• [25] S. Y. Musa, B. A. Asaad, Hypersoft topological spaces, Neutrosophic Sets and Systems, 49 (2022), 397–415
  • View Article
  • Google Scholar


• [26] S. Nazmul, S. K. Samanta, Neigbourhood properties of soft topological spaces, Ann. Fuzzy Math. Infor., 6 (2013), 1–15
  • View Article
  • Google Scholar


• [27] Z. Pawlak, Rough sets, Internat. J. Comput. Inform. Sci., 11 (1982), 341–356
  • View Article
  • MathSciNet


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


• [29] L. A. Zadeh, Fuzzy set, Information and Control, 8 (1965), 338–353
  • View Article
  • Google Scholar
  • MATH