A note on bipolar soft supra topological spaces. (English) Zbl 1530.54002
Summary: In this paper, we introduce the concept of bipolar soft supra topological space and provide a characterization of the related concepts of bipolar soft supra closure and bipolar soft supra interior. We also establish a connection between bipolar soft supra topology and bipolar soft topology. Additionally, we present the concept of bipolar soft supra continuous mapping and examine the concept of bipolar soft supra compact topological space. A related result concerning the image of the bipolar soft supra compact space is proved. Finally, we identify the concepts of disconnected (connected) and strongly disconnected (strongly connected) space and derive several results linking them together. Relationships among these concepts are clarified with the aid of examples.
MSC:
| 54A05 | Topological spaces and generalizations (closure spaces, etc.) |
| 54A40 | Fuzzy topology |
| 03E20 | Other classical set theory (including functions, relations, and set algebra) |
| 03E75 | Applications of set theory |
| 54D05 | Connected and locally connected spaces (general aspects) |
Keywords:
bipolar soft supra topological space; bipolar soft supra closure; bipolar soft supra interior; disconnected space; strongly disconnected spaceReferences:
| [1] | S.E. Abbas: Intuitonistic supra fuzzy topological spaces. Chaos Solitions and Fractals 21 (2004), 1205-1214. https://doi.org/10.1016/j.chaos.2003.12.070 · Zbl 1060.54501 |
| [2] | M.E. Abd-Elmonsef & A. Ramadan: On fuzzy supra topological spaces. Indian J. Pure Appl. Math. 18 (1987), 322-329. · Zbl 0617.54004 |
| [3] | M. Abo-Elhamayed & T.M. Al-Shami: Supra homeomorphism in supra topological ordered spaces. Facta Universitatis, Series: Mathematics and Informatics 31 (2016), no. 5, 1091-1106. doi:10.22190/FUMI1605091A · Zbl 1461.54060 |
| [4] | U. Acar, F. Koyuncu & B. Tanay: Soft sets and soft rings. Comput. Math. Appl. 59 (2010), 3458-3463. https://doi.org/10.1016/j.camwa.2010.03.034 · Zbl 1197.03048 |
| [5] | M. Akram & F. Feng: Soft intersection Lie algebras. Quasigroups and Related Systems 21 (2013), 1-10. · Zbl 1358.17035 |
| [6] | T.M. Al-Shami & M.E. El-Shafei: Two types of separation axioms on supra soft topological spaces. Demonstratio Mathematica 52 (2019), no. 1, 147-165. https://doi.org/10.1515/dema-2019-0016 · Zbl 1423.54047 |
| [7] | T.M. Al-Shami & M.E. El-Shafei: On supra soft topological ordered spaces. Arab Journal of Basic and Applied Sciences 26 (2019), no. 1, 433-445. https://doi.org/10.1080/25765299.2019.1664101 · Zbl 1423.54047 |
| [8] | T.M. Al-Shami & I. Alshammari: Rough sets models inspired by supra-topology structures. Artificial Intelligence Review 56 (2023), 6855-6883. https://doi.org/10.1007/s10462-022-10346-7 |
| [9] | T.M. Al-Shami, J.C.R. Alcantud & A.A. Azzam: Two New Families of Supra-Soft Topological Spaces Defined by Separation Axioms. Mathematics 10 (2022), no. 23, 4488. https://doi.org/10.3390/math10234488 |
| [10] | B.A. Asaad, T.M. Al-Shami & El-Sayed A. Abo-Tabl: Applications of some operators on supra topological spaces. Demonstratio Mathematica 53 (2020), no. 1, 292-308. https://doi.org/10.1515/dema-2020-0028 · Zbl 1457.54001 |
| [11] | T.M. Al-Shami: Homeomorphism and Quotient Mappings in Infrasoft Topological Spaces. Journal of Mathematics, vol. (2021), Article ID 3388288, 10 pages. https://doi.org/10.1155/2021/3388288 · Zbl 1477.54005 |
| [12] | J.C.R. Alcantud, T.M. Al-Shami & A.A. Azzam: Caliber and Chain Conditions in Soft Topologies. Mathematics 9 (2021), no. 19, 2349. https://doi.org/10.3390/math9192349 |
| [13] | S. Bayramov & C. Gunduz: Soft locally compact spaces and soft paracompact spaces. J. Math. System Sci. 3 (2013), 122-130. · Zbl 1299.54019 |
| [14] | S. Bayramov & C. Gunduz Aras: On intuitionistic fuzzy soft topolgical spaces. TWMS J. Pure Appl. Math. 5 (2014), no. 1, 66-79. · Zbl 1354.54008 |
| [15] | N. Cagman, S.Karatas & S. Enginoglu: Soft topology. Comput. Math. Appl. 62 (2011), no. 1, 351-358. https://doi.org/10.1016/j.camwa.2011.05.016 · Zbl 1228.03024 |
| [16] | S.A. El-Sheikh & A.M. Abd El-latif: Decompositions of some types of supra soft sets and soft continuity. Int. J. Math. Trends and Tech. 9 (2014), no. 1, 37-56. DOI:10. 14445/22315373/IJMTT-V9P504 · doi:10.14445/22315373/IJMTT-V9P504 |
| [17] | M.E. El-Shafei, M. Abo-Elhamayel & T.M. Al-Shami: Further notions related to new operators and compactness via supra soft topological spaces. International Journal of Advances in Mathematics 2019 (2019), no. 1, 44-60. |
| [18] | A. Fadel & S.C. Dzul-Kifli: Bipolar soft functions. AIMS Mathematics 6 (2021), no. 5, 4428-4446. doi:10.3934/math.2021262 · Zbl 1484.03116 |
| [19] | F. Feng, Y.B. Jun & X. Zhao: Soft semirings. Comput. Math. Appl. 56 (2008), 2621-2628. https://doi.org/10.1016/j.camwa.2008.05.011 · Zbl 1165.16307 |
| [20] | C. Gunduz Aras: A study on intuitionistic fuzzy soft supra topological spaces. Proc. of the Inst. of Math. and Mech. 44 (2018), no. 2, 187-197. · Zbl 1425.54004 |
| [21] | C. Gunduz Aras & S. Bayramov: Results of some separation axioms in supra soft topological spaces. TWMS Journal of Applied and Engineering Mathematics 9 (2019), no. 1, 3479-3486. · Zbl 1499.54009 |
| [22] | C. Gunduz Aras & S. Bayramov: Separation axioms in supra soft topological spaces. Filomat 32 (2018), no. 10, 3479-3486. https://doi.org/10.2298/FIL1810479G · Zbl 1499.54009 |
| [23] | C.G. Aras, T.M. Al-shamib, A. Mhemdic & S. Bayramov: Local compactness and paracompactness on bipolar soft topological spaces. Journal of Intelligent & Fuzzy Systems 43 (2022), 6755-6763. DOI: 10.3233/JIFS-220834 |
| [24] | C. Gunduz Aras & S. Bayramov: On the Tietze extension theorem in soft topological spaces. Proc. of the Inst. of Math. and Mech. 43 (2017), no. 1, 105-115. · Zbl 1380.54018 |
| [25] | S. Hussain & B. Ahmad: Some properties of soft topological spaces. Comput. Math. Appl. 62 (2011), no. 11, 4058-4067. https://doi.org/10.1016/j.camwa.2011.09.051 · Zbl 1236.54007 |
| [26] | P.K. Maji & A.R. Roy: An application of soft sets in a decision making problem. Comput. Math. Appl. 44 (2002), 1077-1083. https://doi.org/10.1016/S0898-1221(02)00216-X · Zbl 1044.90042 |
| [27] | P.K. Maji, R. Biswas & A.R. Roy: Soft Set Theory. Comput. Math. Appl. 45 (2003), 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6 · Zbl 1032.03525 |
| [28] | A.S. Mashhour, A.A. Allam, F.S. Mahmoud & F.H. Khedr: On supra topological spaces. Indian J. Pure App. Math. 14 (1983), no. 4, 502-510. · Zbl 0511.54003 |
| [29] | W.K. Min: A note on soft topological spaces. Comput. Math. Appl. 62 (2011), no. 9, 3524-3528. https://doi.org/10.1016/j.camwa.2011.08.068 · Zbl 1236.54008 |
| [30] | D. Molodtsov: Soft set theory-First results. Comput. Math. Appl. 37 (1999), no. 4/5, 19-31. · Zbl 0936.03049 |
| [31] | S. Oztunc, S. Aslan & H. Dutta: Categorical structures of soft groups. Soft Comput. 25 (2021), 3059-3064. https://doi.org/10.1007/s00500-020-05362-0 · Zbl 1491.20185 |
| [32] | S. Oztunc: Some Properties of Soft Categories. International Journal of Modeling and Optimization 6 (2016), no. 2, 91-95. DOI:10.7763/IJMO.2016.V6.510 |
| [33] | T.Y. Ozturk: On bipolar soft points. TWMS J. Appl. Eng. Math. 10 (2020), no. 4, 877-885. |
| [34] | M. Shabir &], M. Naz: On bipolar soft sets. (2013), Retrieved from https://arxiv.org/abs/1303.1344v1. · Zbl 1305.03048 |
| [35] | 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 · Zbl 1219.54016 |
| [36] | M. Shabir & A. Bakhtawar: Bipolar soft connected, bipolar soft disconnected and bipolar soft compact spaces. Songklanakarin J. Sci. Technol. 39 (2017), no. 3, 359-371. |
| [37] | N. Turanli: An overwiev of intuitionistic fuzzy supra topological spaces. Hacettepe J. of Math. Statistics 32 (2003), 17-26. Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/55282/759933 · Zbl 1079.54009 |
| [38] | I. Zorlutuna, M. Akdag, W.K. Min & S. Atmaca: Remarks on soft topological spaces. Ann. Fuzzy Math. Inform. 3 (2012), no. 2, 171-185. · Zbl 1301.54031 |
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