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Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

On Ri spaces with α(γos, γ¢os)-open sets

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pp. 1919–1933Vol. 29Issue 6June 2026DOI: 10.47974/JIM-2409XML
Received:
01 Nov 2025
Published Online:
30 Jun 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2409
Pages:
1919–1933

Abstract

An innovative collection of openR setsR, specifically αγos-openR setsR are offered by this paper authors and its rudimentary properties utilizing the respective τγos-interiorR and τγos- closureR operatorsR are premeditated in their previous papers. As well, it has been substantiated that the idea of γos-openR setsR besides αγos - openR setsR are autonomous and each γos-openR setR is an αos openR setR, but the contrary need not be exact. The perceptions of αγos Ti spacesR also their properties are familiarized and recognized the connection among these spacesR  by establishing several Theorems, undistinguishable statements, consequences besides corollaries. Another new collection of openR setsR namely α(γos, γ¢os)-openR setsR was introduced and their properties were presented with the corresponding interiorR and closureR operators. Further the idea of α(γos, γ¢os) Ti spacesR were adapted and documented the connection among these spaces by providing several theorems.   The theory of α(γos, γ¢os) Ri spacesR have been familiarized and their descriptions have been premeditated by illustrating τα(γos, γ¢os) -kernel and several statements comprehend to that idea. Also the association amongst these α(γos, γ¢os) Ri spacesR have been formed and evaluated by means of several axioms and opposite affirmations.

Keywords

Subject Classifications

54A0554A10

References

[1] O. Njȧstad, “On some classes of nearly open sets,” Pacific Journal of Mathematics, vol. 15, no. 3, pp. 961–970 (1965), doi: 10.2140/ pjm.1965.15.961.
[2] N. Levine, “Semi-open sets and semi-continuity in topological spaces,” The American Mathematical Monthly, vol. 70, no. 1, pp. 36–41 (1963), doi: 10.1080/00029890.1963.11990064. 
[3] H. H. Corson and E. Michael, “Metrizability of certain countable unions,” Illinois Journal of Mathematics, vol. 8, no. 2, pp. 351–360 (1964), doi: 10.1215/ijm/1256059919.
[4] D. Andrijević, “On the topology generated by preopen sets,” Matematički Vesnik, vol. 39, pp. 367–376 (1987).
[5] S. Kasahara, “Operation-compact spaces,” Mathematica Japonica, vol. 24, pp. 97–105 (1979).
[6] H. Ogata, “Operations on topological spaces and associated topology,” Mathematica Japonica, vol. 36, pp. 175–184 (1991).
[7] G. S. S. Krishnan, “On γ-semi-open sets in topological spaces,” Bulletin of the Calcutta Mathematical Society, vol. 98, pp. 517–530 (2006).
[8] G. Krishnan and K. Balachandran, “On a class of γ-preopen sets in a topological space,” East Asian Mathematical Journal, vol. 22, no. 2, pp. 131–149 (2006).
[9] N. Kalaivani and G. S. S. Krishnan, “Operation approaches on α-γ-open sets in topological spaces,” International Journal of Mathematical Analysis, vol. 7, no. 10, pp. 491–498 (2013).
[10] N. Kalaivani and D. Saravanakumar, “Certain separation axioms and R spaces with on αγO_{\gamma_O}γO-open sets,” in Proceedings of the First International Conference on Mathematical Modeling and Computational Science, S. L. Peng, R. X. Hao, and S. Pal, Eds., Advances in Intelligent Systems and Computing, vol. 1292, pp. 601–613 (2021), doi: 10.1007/978-981-33-6407-5_54.
[11] N. Kalaivani and D. Saravanakumar, “Operation connected spaces, compact spaces with α(γ,γ′)-open sets in topological spaces,” AIP Conference Proceedings, vol. 2112, p. 020025 (2019), doi: 10.1007/978-981-33-6407-5_54.
[12] N. Kalaivani, A. I. El-Maghrabi, D. Saravanakumar, and G. Sai Sundara Krishnan, “Operation-compact spaces, regular spaces and normal spaces with α-γ-open sets in topological spaces,” Journal of Interdisciplinary Mathematics, vol. 20, no. 2, pp. 427–441 (2017), doi: 10.1080/09720502.2015.1104945.
[13] A. A. Nasef, A. I. El-Maghrabi, and M. A. Abd El-Monsef, “Bi-nano topological spaces with grill bi-open sets,” Journal of Interdisciplinary Mathematics, vol. 23, no. 1, pp. 149–160 (2020), doi: 10.1080/09720502.2019.1706920.
[14] A. A. Nasef, A. I. El-Maghrabi, and M. A. Abd El-Monsef, “Some covering properties and connectedness via generalized α-sets,” Journal of Interdisciplinary Mathematics, vol. 22, no. 6, pp. 1023–1036 (2019), doi: 10.1080/09720502.2019.1630563.
[15] A. A. Nasef, A. I. El-Maghrabi, and M. A. Abd El-Monsef, “On semi-open sets in grill nano topological spaces,” Journal of Interdisciplinary Mathematics, vol. 22, no. 5, pp. 807–819 (2019), doi: 10.1080/09720502.2019.1593947.

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