Separation Axioms Defined by Four Different Points in Neutrosophic Crisp Spaces

Nour M.; L. A. A.; Ali H. M.

doi:https://doi.org/10.54216/IJNS.270109

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Volume 27 • Issue 1 • PP: 93-99 • 2026

Separation Axioms Defined by Four Different Points in Neutrosophic Crisp Spaces

Nour M. Easi ^1*

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,

L. A. A. Jabar ¹

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,

Ali H. M. Al-Obaidi ¹

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¹Department of Mathematics, College of Education for Pure Science, University of Babylon, Iraq

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.270109

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Received: March 29, 2025 Revised: June 08, 2025 Accepted: July 20, 2025

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Abstract

In this paper, separation axioms are discussed in neutrosophic crisp topological spaces from a new perspective. This is generally useless because any neutrosophic set does not necessarily have a union of its neutrosophic points under any union and for any kind of points. Hence, the separation properties are studied concerning stable neutrosophic crisp topological spaces, which are determined by two special types of complement. Moreover, various examples are illustrated in these cases.

Keywords

Neutrosophic crisp sets Neutrosophic crisp points Stable neutrosophic crisp topological space stable closure neutrosophic T_i-Space i=0 1 2

References

[1] M. H. Hadi and L. A. A. Al-Swidi, “The Neutrosophic Axial Set Theory,” Neutrosophic Sets and Systems, vol. 51, pp. 295-302, 2022.

[2] A. A. Salama, F. Smarandache, and V. Kroumov, “Neutrosophic Crisp Sets and Neutrosophic Crisp Topological Spaces,” Neutrosophic Sets and Systems, vol. 2, no. 1, pp. 25-30, 2014.

[3] A. Y. K. Mutawek and R. A. H. Al-Abdulla, “Ideal Grill Compactness Space,” Journal of Interdisciplinary Mathematics, vol. 26, no. 4, 2023.

[4] Z. F. A. Alhussain and A. F. Hassan, “A Binary Relation Fuzzy Soft Matrix-Theoretic Approach to Image Quality Measurement: Comparison with Statistical Similarity Metrics,” Mathematical Modelling of Engineering Problems, vol. 10, no. 3, pp. 799-804, 2023.

[5] Q. H. Hatem, M. M. Abdulkadhim, A. H. M. Al-Obaidi, and S. Broumi, “Neutrosophic Crisp Generalized sg-Closed Sets and Their Continuity,” International Journal of Neutrosophic Science, vol. 20, no. 3, pp. 106-118, 2023. doi: 10.54216/IJNS.200408.

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Easi, Nour M., Jabar, L. A. A., Al-Obaidi, Ali H. M.. "Separation Axioms Defined by Four Different Points in Neutrosophic Crisp Spaces." International Journal of Neutrosophic Science, vol. Volume 27, no. Issue 1, 2026, pp. 93-99. DOI: https://doi.org/10.54216/IJNS.270109

Easi, N., Jabar, L., Al-Obaidi, A. (2026). Separation Axioms Defined by Four Different Points in Neutrosophic Crisp Spaces. International Journal of Neutrosophic Science, Volume 27(Issue 1), 93-99. DOI: https://doi.org/10.54216/IJNS.270109

Easi, Nour M., Jabar, L. A. A., Al-Obaidi, Ali H. M.. "Separation Axioms Defined by Four Different Points in Neutrosophic Crisp Spaces." International Journal of Neutrosophic Science Volume 27, no. Issue 1 (2026): 93-99. DOI: https://doi.org/10.54216/IJNS.270109

Easi, N., Jabar, L., Al-Obaidi, A. (2026) 'Separation Axioms Defined by Four Different Points in Neutrosophic Crisp Spaces', International Journal of Neutrosophic Science, Volume 27(Issue 1), pp. 93-99. DOI: https://doi.org/10.54216/IJNS.270109

Easi N, Jabar L, Al-Obaidi A. Separation Axioms Defined by Four Different Points in Neutrosophic Crisp Spaces. International Journal of Neutrosophic Science. 2026;Volume 27(Issue 1):93-99. DOI: https://doi.org/10.54216/IJNS.270109

N. Easi, L. Jabar, A. Al-Obaidi, "Separation Axioms Defined by Four Different Points in Neutrosophic Crisp Spaces," International Journal of Neutrosophic Science, vol. Volume 27, no. Issue 1, pp. 93-99, 2026. DOI: https://doi.org/10.54216/IJNS.270109

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