Further properties of soft somewhere dense continuous functions and soft Baire spaces

Volume 32, Issue 1, pp 54--63 http://dx.doi.org/10.22436/jmcs.032.01.05

Publication Date: July 11, 2023 Submission Date: May 13, 2023 Revision Date: May 29, 2023 Accteptance Date: June 09, 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)

• 346 Downloads
• 956 Views

Authors

Z. A. Ameen - Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq. R. Abu-Gdairi - Department of Mathematics, Faculty of Science, Zarqa University, P.O. Box 13110, Zarqa, Jordan. T. M. Al-Shami - Department of Mathematics, Sana'a University, P.O. Box 1247, Sana'a, Yemen. - Department of Engineering Mathematics \(\&\) Physics, Faculty of Engineering \(\&\) Technology, Future University, Duhok, Egypt. B. A. Asaad - Department of Mathematics, Faculty of Science, University of Zakho, Zakho 42002, Iraq. - Department of Computer Science, College of Science, Cihan University-Duhok, Iraq. M. Arar - Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi Arabia.

Abstract

In this paper, we first explore more properties of soft somewhere dense continuous functions. Then, we discuss the preservation of soft Baire property and soft Baire category. We give some concrete examples to illustrate how our findings extend some conclusions and connections made in the literature.

Share and Cite

Keywords

• Soft continuous
• soft somewhat continuous
• soft semicontinuous
• soft somewhere dense continuous
• fuzzy Baire space
• soft Baire space

MSC

•  54C08
•  54C10
•  54E52
•  03E72

References

• [1] U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59 (2010), 3458–3463
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


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


• [3] J. C. R. Alcantud, Soft open bases and a novel construction of soft topologies from bases for topologies, Mathematics, 8 (2020), 1–12
  • View Article
  • Google Scholar


• [4] J. C. R. Alcantud, An operational characterization of soft topologies by crisp topologies, Mathematics, 9 (2021), 1–12
  • View Article
  • Google Scholar


• [5] J. C. R. Alcantud, T. M. Al-shami, A. A. Azzam, Caliber and chain conditions in soft topologies, Mathematics, 9 (2021), 1–15
  • View Article
  • Google Scholar


• [6] S. Al Ghour, Soft complete continuity and soft strong continuity in soft topological spaces, Axioms, 12 (2023), 1–14
  • View Article
  • Google Scholar


• [7] S. Al Ghour, Z. A. Ameen, On soft submaximal spaces, Heliyon, 8 (2022), 5 pages
  • View Article
  • Google Scholar


• [8] S. Al-Ghour, Z. A. Ameen, Maximal soft compact and maximal soft connected topologies, Appl. Comput. Intell. Soft Comput., 2022 (2022), 7 pages
  • View Article
  • Google Scholar


• [9] M. I. Ali, F. Feng, X. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), 1547–1553
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] H. H. Al-jarrah, A. Rawshdeh, T. M. Al-shami, On soft compact and soft Lindel¨of spaces via soft regular closed sets, Afr. Mat., 33 (2022), 16 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] T. M. Al-shami, Soft somewhere dense sets on soft topological spaces, Commun. Korean Math. Soc., 33 (2018), 1341– 1356
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] T. M. Al-shami, Comments on some results related to soft separation axioms, Afr. Mat., 31 (2020), 1105–1119
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] T. M. Al-shami, Soft somewhat open sets: Soft separation axioms and medical application to nutrition, Comput. Appl. Math., 41 (2022), 22 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] T. M. Al-shami, I. Alshammari, B. A. Asaad, Soft maps via soft somewhere dense sets, Filomat, 34 (2020), 3429–3440
  • View Article
  • Google Scholar
  • MATH


• [15] T. M. Al-shami, Z. A. Ameen, R. Abu-Gdairi, A. Mhemdi, On primal soft topology, Mathematics, 11 (2023), 1–15
  • View Article
  • Google Scholar


• [16] T. M. Al-shami, Z. A. Ameen, B. A. Asaad, A. Mhemdi, Soft bi-continuity and related soft functions, J. Math. Comput. Sci., 30 (2023), 19–29
  • View Article
  • Google Scholar


• [17] T. M. Al-shami, Z. A. Ameen, A. A. Azzam, M. E. El-Shafei, Soft separation axioms via soft topological operators, AIMS Math., 7 (2022), 15107–15119
  • View Article
  • MathSciNet
  • Google Scholar


• [18] T. M. Al-shami, Z. A. Ameen, A. Mhemdi, The connection between ordinary and soft -algebras with applications to information structures, AIMS Math., 8 (2023), 14850–14866
  • View Article
  • Google Scholar


• [19] A. A. Allam, T. H. Ismail, R. A. Mohammed, A new approach to soft belonging, Ann. Fuzzy Math. Inform., 13 (2017), 145–152
  • View Article
  • Google Scholar
  • MATH


• [20] Z. A. Ameen, A non-continuous soft mapping that preserves some structural soft sets, J. Intell. Fuzzy Syst., 42 (2022), 5839–5845
  • View Article
  • Google Scholar


• [21] Z. A. Ameen, S. Al Ghour, Extensions of soft topologies, Filomat, 36 (2022), 5279–5287
  • View Article
  • MathSciNet
  • Google Scholar


• [22] Z. A. Ameen, S. Al Ghour, Minimal soft topologies, New Math. Nat. Comput., 19 (2023), 19–31
  • View Article
  • Google Scholar


• [23] Z. A. Ameen, T. M. Al-shami, R. Abu-Gdairi, A. Mhemdi, The Relationship between ordinary and soft algebras with an application, Mathematics, 11 (2023), 1–12
  • View Article
  • Google Scholar


• [24] 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
  • View Article
  • Google Scholar


• [25] Z. A. Ameen, A. B. Khalaf, The invariance of soft Baire spaces under soft weak functions, J. Interdiscip. Math., 25 (2022), 1295–1306
  • View Article
  • Google Scholar


• [26] B. A. Asaad, Results on soft extremally disconnectedness of soft topological spaces, J. Math. Comput. Sci., 17 (2017), 448–464
  • View Article
  • Google Scholar
  • MATH


• [27] 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
  • View Article
  • Google Scholar


• [28] A. Ayg¨unoˇ glu, H. Ayg¨ un, Some notes on soft topological spaces, Neural Comput. Appl., 21 (2012), 113–119
  • View Article
  • Google Scholar


• [29] A. A. Azzam, Z. A. Ameen, T. M. Al-shami, M. E. El-Shafei, Generating soft topologies via soft set operators, Symmetry, 14 (2022), 1–13
  • View Article
  • Google Scholar


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


• [31] 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


• [32] J. Dobos, A note on the invariance of Baire spaces under mappings, Cˇ asopis Peˇst. Mat., 108 (1983), 409–411
  • View Article
  • Google Scholar
  • MATH


• [33] J. Doboˇs, Z. Piotrowski, I. L. Reilly, Preimages of Baire spaces, Math. Bohem., 119 (1994), 373–379
  • View Article
  • Google Scholar
  • MATH


• [34] M. E. El-Shafei, M. Abo-Elhamayel, T. M. Al-shami, Partial soft separation axioms and soft compact spaces, Filomat, 32 (2018), 4755–4771
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [35] M. E. El-Shafei, T. M. Al-shami, Applications of partial belong and total non-belong relations on soft separation axioms and decision-making problem, Comput. Appl. Math., 39 (2020), 17 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [36] 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
  • View Article
  • Google Scholar


• [37] Z. Frol´ık, Baire spaces and some generalizations of complete metric spaces, Czechoslovak Math. J., 11 (1961), 237–248
  • View Article
  • Google Scholar


• [38] Z. Frol´ık, Remarks concerning the invariance of Baire spaces under mappings, Czechoslovak Math. J., 11 (1961), 381–385
  • View Article
  • Google Scholar
  • MATH


• [39] R. C. Haworth, R. A. McCoy, Baire spaces, Dissertationes Math., 141 (1977), 73 pages
  • View Article
  • Google Scholar


• [40] S. Hussain, B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl., 62 (2011), 4058–4067
  • View Article
  • MathSciNet
  • Google Scholar


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


• [42] F. Lin, Soft connected spaces and soft paracompact spaces, Int. J. Math. Comput. Sci., 7 (2013), 277–283
  • View Article
  • Google Scholar


• [43] J. Mahanta, P. K. Das, On soft topological space via semiopen and semiclosed soft sets, Kyungpook Math J., 4 (2014), 221–223
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


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


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


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


• [47] A. A. Rawshdeh, H. H. Al-Jarrah,, T. M. Al-shami, Soft expandable spaces, Filomat, 37 (2023), 2845–2858
  • View Article
  • MathSciNet
  • Google Scholar


• [48] M. Riaz, F. Zain, Certain properties of soft metric spaces, J. Fuzzy Math., 25 (2017), 543–560
  • View Article
  • Google Scholar
  • MATH


• [49] W. Rong, The countabilities of soft topological spaces, Int. J. Comput. Math. Sci., 6 (2012), 952–955
  • View Article
  • Google Scholar


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


• [51] M. Terepeta, On separating axioms and similarity of soft topological spaces, Soft Comput., 23 (2019), 1049–1057
  • View Article
  • Google Scholar
  • MATH


• [52] G. Thangaraj, S. Anjalmose, On fuzzy Baire spaces, J. Fuzzy Math., 21 (2013), 667–676
  • View Article
  • Google Scholar
  • MATH


• [53] Y. Yumak, A. K. Kaymakci, Soft -open sets and their applications, J. New Theory, 4 (2015), 80–89
  • View Article
  • Google Scholar