Separation axioms via ideal in Ri*-open sets
*Mahmoud M. Al-HadidiCorresponding authormahmoud.radi2203@ihcoedu.uobaghdad.edu.iqDepartment of Mathematics College of Education for Pure Science (Ibn Al-Haitham) University of BaghdadBaghdad, IraqView full profile → , Rana B. Esmaeelrana.b.i@ihcoedu.uobaghdad.edu.iqDepartment of Mathematics College of Education for Pure Science (Ibn Al-Haitham) University of BaghdadDepartment of Mathematics College of Education for Pure Sciences (Ibn Al-Haitham) University of BaghdadBaghdad, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Jan 2026
- Published Online:
- 27 Jun 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2593
- Pages:
- 1359–1364
Abstract
Keywords
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References
[1] R. Vaidyanathaswamy, “The Localization theory in set topology,” in Proc. Indian Academy Sci, pp. 51–61 (1960).
[2] T. R. Hamlett and D. Janković, “Compactness with Respect to an Ideal.” Bulletin of the Italian Mathematical Union, Series VII B, vol. 4‑B, pp. 849–861 (1990).
[3] T. R. Hamlett and D. Jankovic, “Ideals in topological spaces and the set operator ψ,” Bulletin of the Italian Mathematical Union, vol. 7, pp. 863–874 (1990).
[4] A. I. Naser and R. B. Esmaeel, “On α‑J‑space,” Journal of Advanced Research in Dynamical and Control Systems, vol. 11, no. 1, Special Issue, pp. 1379–1382 (2019).
[5] M. Parimala, S. Jafari, and S. Murali, “Nano ideal generalized closed sets in nano ideal topological spaces,” Annales Univ. Sci. Budapest, vol. 60, pp. 3–11 (2019).
[6] İ. Rajasekaran and O. Nethaji, “Simple Forms of Nano Open Sets in an Ideal Nano Topological Spaces,” Journal of New Theory, no. 24, pp. 35–43 (2018).
[7] M. Parimala, S. Jafari, and S. Murali, “Nano ideal generalized closed sets in nano ideal topological spaces,” Annales Univ. Sci. Budapest, vol. 60, pp. 3–11 (2019).
[8] I. Rajasekaran and O. Nethaji, “Simple forms of nano open sets in an ideal nano topological space,” Journal of New Theory, no. 24, pp. 35–43 (2019).
[9] J. Dontchev, “On Harsdorf Spaces via Ideals and I-Irresolute Functions,” Annals of the New Academy of Sciences, vol. 767, pp. 28–38 (1995).
[10] M. A. Karim and A. I. Nasir, “Separation Axioms via Ǐ Semi g Open Sets,” Ibn AL-Haitham Journal for Pure and Applied Science, vol. 33, no. 1, pp. 157–161 (2020).
[11] A. Kandil, O. El-Tantawy, and A. M. A. El-latif “Soft Ideal theory soft local function and Generated soft Topological spaces,” Appl. Math. Inf. Sci, vol. 8, no. 4, pp. 1595–1603 (2014).
[12] E. A. A. K. Mohsin, Y. Y. Yousif, and M. E. Sayed, “Some Results on Nano Perfect Mappings,” Ibn AL-Haitham Journal for Pure and Applied Sciences, vol. 36, no. 3, pp. 398–407 (2020).
[13] E. Ekici and T. Noiri, “Connectedness in ideal topological spaces,” Novi Sad J. Math, vol. 38, no. 2, pp. 65–70 (2008).
[14] I. Rajasekaran and O. Nethaji, “Simple Forms of Nano Open sets in an Ideal nano Topological space,” Journal of New Theory, no. 24, pp. 35–43 (2018).
[15] M. Parimala, S. Jafari, and S. Murali, “Nano ideal generalized closed sets in nano ideal topological spaces,” Annales Univ. Sci. Budabest, vol. 60, pp. 3–11 (2019).
[16] O. Ravi, S. Tharmar, M. Sangeetha, and J. Antony Rex Rodrigo, “g–closed sets in ideal topological spaces,” Jordan Journal of Mathematics and Statistics, vol. 6, no. 1, pp. 1–13 (2013).
[17] J. C. Ramos-Fernández, E. Rosas, and M. Salas-Brown, “Exploring generalized h-open sets,” Journal of Interdisciplinary Mathematics (2026), doi: 10.47974/JIM-2185.
[18] R. B. Esmaeel and M. O. Mustafa, “Separation axioms with grill-topological open set,” J. Phys. Conf. Ser., vol. 1879, no. 2, p. 22107 (2021).
[19] R. A. Hosny, M. K. El-Bably, and M. A. El-Gayar, “Primal approximation spaces by κ-neighborhoods with applications,” European Journal of Pure and Applied Mathematics, vol. 18, no. 1, p. 5827 (2024), doi: 10.29020/nybg.ejpam.v18i1.5827.




