1
Department of Mathematics, College of Education for Pure Science, University of Babylon, Hillah, Iraq.
(doaa.tuama.pure526@student.uobabylon.edu.iq)
2
Department of Mathematics, College of Education for Pure Science, University of Babylon, Hillah, Iraq.
(pure.leal.abd@uobabylon.edu.iq)
Abstract :
The general direction for generating any stable neutrosophic crisp topology is through base or the stable neutrosophic crisp interior concept, which is closed in the finite intersection process and not closed in the union process, likewise the stable neutrosophic crisp exterior is closed in the finite union process but not closed in finite intersection. Our research deals with finding necessary and sufficient condition for the finite union and finite intersection to be closed respectively using the concept of confused crisp sets.
Keywords :
Stable Neutrosophic Crisp Topological Spaces; Stable Neutrosophic Crisp Interior Set; Stable Neutrosophic Crisp Exterior Set; Confused Crisp Set.
References :
[1] Salama, A. A., & Smarandache, F. (2015). Neutrosophic crisp set theory. Infinite Study.
[2] Karatas, S., & Kuru, C. (2016). Neutrosophic topology. Neutrosophic sets and systems, 13(1), 90-95.
[3] Salama, A. A., Hanafy, I. M., Elghawalby, H., & Dabash, M. S. (2016). Neutrosophic Crisp α-Topological Spaces. Neutrosophic Sets and Systems, 12, 92-96.
[4] Al-Hamido, R. K. (2020). A new approach of neutrosophic topological space. International Journal of neutrosophic Science, 7, 55-61.
[5] Al-Nafee, A. B., Smarandache, F., & Salama, A. A. (2020). New Types of Neutrosophic Crisp Closed Sets. Infinite Study.
[6] Doaa Nihad, L.A.Al Swidi .(2024). Stable Neutrosophic Crisp Topological Space. International of Journal of Neutrosophic Science, 23 (04), 154-159.
[7] AL-Nafee, A. B., Al-Hamido, R. K., & Smarandache, F. (2019). Separation axioms in neutrosophic crisp topological spaces. Infinite Study.
[8] Doaa Nihad, L.A. Al Swidi , “Confused crisp set stable neutrosophic topological spaces ”, In AIP Conference Proceedings . unpublished.
[9] Al-Swidi, L., & AL-Ethary, M. A. (2014). Compactness with" Gem-Set. Int. Journal of Math. Analysis, 8(23), 1105-1117.
[10] Al-Swidi, L. A. A. H., & Al-Fatlawe, I. J. (2010). On Semiparacompactness and z-paracompactness in Bitopological Spaces. European Journal of Scientific Research, 47(4), 554-561.
[11] Al-Swidi, L. A. (2010). On preparacompactness in bitopological spaces. European journal of scientific research, 201046(2), 165-171.
[12] Q. H. Imran, A. H. M. Al-Obaidi, F. Smarandache and Md. Hanif PAGE, On some new concepts of weakly neutrosophic crisp separation axioms. Neutrosophic Sets and Systems, 51(2022), 330-343.
[13] Q. H. Imran, M. M. Abdulkadhim, A. H. M. Al-Obaidi and Said Broumi, Neutrosophic crisp generalized sg-closed sets and their continuity. International Journal of Neutrosophic Science, 20(4) (2023), 106-118.
[14] M. M. Abdulkadhim, Q. H. Imran, A. H. M. Al-Obaidi and Said Broumi, On neutrosophic crisp generalized alpha generalized closed sets. International Journal of Neutrosophic Science, 19(1) (2022), 107-115.
[15] M. M. Abdulkadhim, Q. H. Imran, A. K. Abed and Said Broumi, On neutrosophic generalized alpha generalized separation axioms. International Journal of Neutrosophic Science, 19(1) (2022), 99-106.
[16] Dieudonné, J. (1944). Une généralisation des espaces compacts. Journal de Mathematiques pures et appliquées, 23, 65-76.
| Style | # |
|---|---|
| MLA | Doaa Nihad Tomma, L. A. A. Al-Swidi. "Necessary and Sufficient Conditions for a Stability of the Concepts of Stable Interior and Stable Exterior via Neutrosophic Crisp Sets." International Journal of Neutrosophic Science, Vol. 24, No. 1, 2024 ,PP. 87-93 (Doi : https://doi.org/10.54216/IJNS.240108) |
| APA | Doaa Nihad Tomma, L. A. A. Al-Swidi. (2024). Necessary and Sufficient Conditions for a Stability of the Concepts of Stable Interior and Stable Exterior via Neutrosophic Crisp Sets. Journal of International Journal of Neutrosophic Science, 24 ( 1 ), 87-93 (Doi : https://doi.org/10.54216/IJNS.240108) |
| Chicago | Doaa Nihad Tomma, L. A. A. Al-Swidi. "Necessary and Sufficient Conditions for a Stability of the Concepts of Stable Interior and Stable Exterior via Neutrosophic Crisp Sets." Journal of International Journal of Neutrosophic Science, 24 no. 1 (2024): 87-93 (Doi : https://doi.org/10.54216/IJNS.240108) |
| Harvard | Doaa Nihad Tomma, L. A. A. Al-Swidi. (2024). Necessary and Sufficient Conditions for a Stability of the Concepts of Stable Interior and Stable Exterior via Neutrosophic Crisp Sets. Journal of International Journal of Neutrosophic Science, 24 ( 1 ), 87-93 (Doi : https://doi.org/10.54216/IJNS.240108) |
| Vancouver | Doaa Nihad Tomma, L. A. A. Al-Swidi. Necessary and Sufficient Conditions for a Stability of the Concepts of Stable Interior and Stable Exterior via Neutrosophic Crisp Sets. Journal of International Journal of Neutrosophic Science, (2024); 24 ( 1 ): 87-93 (Doi : https://doi.org/10.54216/IJNS.240108) |
| IEEE | Doaa Nihad Tomma, L. A. A. Al-Swidi, Necessary and Sufficient Conditions for a Stability of the Concepts of Stable Interior and Stable Exterior via Neutrosophic Crisp Sets, Journal of International Journal of Neutrosophic Science, Vol. 24 , No. 1 , (2024) : 87-93 (Doi : https://doi.org/10.54216/IJNS.240108) |