Volume 3 • Issue 1 • PP: 34-38 • 2022
Properties of Group Neutro-Topological Space
Open Access & Copyright
© 2022 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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
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
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.