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Journal of Neutrosophic and Fuzzy Systems

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Journal of Neutrosophic and Fuzzy Systems

Volume 3 , Issue 1 , PP: 34-38, 2022 | Cite this article as | XML | Html | PDF

Properties of Group Neutro-Topological Space

Bhimraj Basumatary 1 * , Binod Chandra Tripathy 2

  • 1 Department of Mathematical Sciences, Bodoland University, 783370, Kokrajhar, India - (brbasumatary14@gmail.com)
  • 2 Department Of Mathematics, Tripura University, Agartala, 799022, Tripura, India - (tripathybc@gmail.com)

    • Doi: https://doi.org/10.54216/JNFS.030104

    Received: March 02, 2022 Accepted: May 27, 2022
    Abstract

    Unlike traditional algebraic structures, where all operations are well-defined and all axioms are completely true, NeutroAlgebras and AntiAlgebras allow operations to be partially well-defined and axioms to be partially true or fully outer-defined, and axioms to be completely false. These NeutroAlgebras and AntiAlgebras represent a new research subject based on real-world examples. Since an empty set is not a subgroup of a group by observing this, the article leads to learning group neutro-topological space. We introduced the notion of a group neutro-topological space and investigated its properties.

    Keywords :

    Topological Space , Neutrosophic Set , NeutroAlgebras , Neutro-Topological Space , Group Neutro-Topological Space.

    References

    [1]   Smarandache, F., Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105, 1998.

    [2]   Smarandache, F., Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures, in Advances of Standard and Nonstandard Neutrosophic Theories, Pons Publishing House Brussels, Belgium, Ch. 6, 240-265, 2019.

    [3]   Smarandache, F., Introduction to NeutroAlgebraicstructures and AntiAlgebraicstructures (revisited), Neutrosophic Sets and Systems, 31, 1-16, 2020.

    [4]   Sumathi, I. R. &Arockiarani, I., Topological group structure of the neutrosophic set. Journal of Advanced Studies in Topology, 7(1), 12-20, 2016.

    [5]   Salama, A. A. &Alblowi, S. A., Neutrosophicset and neutrosophic topological spaces. IOSR, Journal of Mathematics, 3(4), 31-35, 2012.

    [6]   Narmada Devi, R., Dhavaseelan, R. & Jafari, S., On separation axioms in an ordered neutrosophic topological space. Neutrosophic Sets and Systems, 18, 27-36, 2017.

    [7]   Sumathi, I. R. &Arockiarani, I., Fuzzy neutrosophic groups. Advanced in Fuzzy Mathematics, 10(2), 117-122, 2015.

    [8]   Mwchahary, D. D. &Basumatary, B., A note on neutrosophic topological space, Neutrosophic Sets and Systems, 33, 134-144, 2020.

    [9]   Smarandache, F., NeutroAlgebrais a generalization of partial algebra. International Journal of Neutrosophic Science (IJNS), 2, 8-17, 2020.

    [10] Şahin, M., Kargin, A. &Yücel, M., Neutro-Topological Space, and Anti-Topological Space, The Educational Publisher Inc., 1091 West 1st Ave., Grandview Heights, OH 43212, United States, 2021.

    [11] Smarandache, F. (2020). Generalizations and Alternatives of Classical Algebraic Structures to NeutroAlgebraic Structures and AntiAlgebraic Structures, Journal of Fuzzy Extension and Applications (JFEA), J. Fuzzy. Ext. Appl., 1(2), 85–87.

    [12] Agboola, A. A. A., Ibrahim, M. A. & Adeleke, E. O., Elementary examination of NeutroAlgebras and AntiAlgebras viz-a-viz the classical number systems. International Journal of Neutrosophic Science (IJNS), 4, 16-19, 2020.

    [13] Agboola, A. A. A., Introduction to NeutroGroups. International Journal of Neutrosophic Science (IJNS), 6, 41-47, 2020.

    [14] Agboola, A. A. A., Introduction to NeutroRings. International Journal of Neutrosophic Science (IJNS), 7, 62-73, 2020.

    [15] Rezaei, A. &Smarandache, F., On Neutro-BE-algebras and Anti-BE-algebras. International Journal of Neutrosophic Science (IJNS), 4, 8-15, 2020.

    [16] Hamidi, M. &Smarandache, F.,Neutro-BCK-Algebra. International Journal of Neutrosophic Science (IJNS), 8, 110-117, 2020.

    [17] Smarandache, F., Rezaei, A. & Kim, H. S., A new trend to extensions of CI-algebras. International Journal of Neutrosophic Science (IJNS), 5(1), 8-15, 2020.

    [18] Agboola, A. A. A., On finite NeutroGroups of type-NG. International Journal of Neutrosophic Science (IJNS), 10(2), 84-95, 2020.

     

    Cite This Article As :
    Bhimraj Basumatary, Binod Chandra Tripathy. "Properties of Group Neutro-Topological Space." Full Length Article, Vol. 3, No. 1, 2022 ,PP. 34-38 (Doi   :  https://doi.org/10.54216/JNFS.030104)
    Bhimraj Basumatary, Binod Chandra Tripathy. (2022). Properties of Group Neutro-Topological Space. Journal of , 3 ( 1 ), 34-38 (Doi   :  https://doi.org/10.54216/JNFS.030104)
    Bhimraj Basumatary, Binod Chandra Tripathy. "Properties of Group Neutro-Topological Space." Journal of , 3 no. 1 (2022): 34-38 (Doi   :  https://doi.org/10.54216/JNFS.030104)
    Bhimraj Basumatary, Binod Chandra Tripathy. (2022). Properties of Group Neutro-Topological Space. Journal of , 3 ( 1 ), 34-38 (Doi   :  https://doi.org/10.54216/JNFS.030104)
    Bhimraj Basumatary, Binod Chandra Tripathy. Properties of Group Neutro-Topological Space. Journal of , (2022); 3 ( 1 ): 34-38 (Doi   :  https://doi.org/10.54216/JNFS.030104)
    Bhimraj Basumatary, Binod Chandra Tripathy, Properties of Group Neutro-Topological Space, Journal of , Vol. 3 , No. 1 , (2022) : 34-38 (Doi   :  https://doi.org/10.54216/JNFS.030104)

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