TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Freq.: MONTHLY - Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Separation axioms via ideal in Ri*-open sets 

* ,

* Corresponding author · click or hover a name for details

pp. 1359–1364Vol. 29Issue 5-AMay 2026DOI: 10.47974/JIM-2593XML
Received:
01 Jan 2026
Published Online:
27 Jun 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2593
Pages:
1359–1364

Abstract

In this study, a novel category of sets, termed Ri*-open sets are presented. Within the context of ideal “topological spaces”, Different types of type Ri*-Continuous functions are also presented, and the relationships between them are studied. This also includes the introduction and study of generalizations of the concept of separation axioms within topological spaces, using the concept of open sets of type Ri* to generalize new classes of separation axioms within ideal topological sp. An examination of these types and their relationships is conducted, and some properties of these concepts are examined.

Keywords

Subject Classifications

54A0554D10

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.

Views: 30Downloads: 8Citations: 0