A Study On Various Relations

Year 2026, Volume: 18 Issue: 1, 281 - 288, 23.02.2026

Ayşe Nur Tunç , Sena Özen Yıldırım

https://doi.org/10.47000/tjmcs.1756370

https://izlik.org/JA56SB27EP

Abstract

In 2023, $\Gamma-\mathfrak{I}-$open, pre$-\Gamma-\mathfrak{I}-$open, $\Gamma_{\Gamma}-$open, and almost $\Gamma-\mathfrak{I}-$open sets were defined and their relationships with each other were searched by Yalaz and Keskin Kaymakçı in [19]. Furthermore, Devika and Thilagavathi introduced an $M^{\ast}$-open set and investigated its relationships with some special sets in topological space in [5]. In this study, we research the relevances of these sets with other some specific sets obtained by the operators $\Gamma$ and $\Psi_{\Gamma}$ in ideal topological spaces.

Keywords

Γ − I−open set , operator Γ , pre−Γ − I−open set

References

• Al-Omari, A., Noiri, T., Local closure functions in ideal topological spaces, Novi Sad J. Math., 43(2)(2013), 139–149.
• Amsaveni, V., Anitha, M., Subramanian, A., New types of semi-open sets, International Journal of New Innovations in Engineering and Technology, 9(4)(2019), 14–17.
• Caldas, M., Jafari, S., Kov´ar, M. M., Some properties of θ-open sets, Divulgaciones Matem´aticas, 12(2)(2004), 161–169.
• Caldas, M., Ganster, M., Georgiou, D. N., Jafari, S., Noiri, T., On θ-semiopen sets and separation axioms in topological spaces, Carpathian J. Math., 24(1)(2008), 13–22.
• Devika, A., Thilagavathi, A., M∗-open sets in topological spaces, International Journal of Mathematics and Its Applications, 4(1-B)(2016), 1–8.
• Goyal, N., Noorie, N.S., θ-closure and T2 12 spaces via ideals, Italian Journal of Pure and Applied Mathematics, 41(2019), 571–583.
• Jankovi´c, D., Hamlett, T.R., New topologies from old via ideals, Amer. Math. Monthly, 97(4)(1990), 295–310.
• Joseph, J.E., θ-closure and θ-subclosed graphs, Math. Chronicle, 8(1979), 99–117.
• Kuratowski, K., Topology, Vol. I, Academic Press, New York, 1966.
• Levine, N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1)(1963), 36–41.
• Natkaniec, T., On I-continuity and I-semicontinuity points, Mathematica Slovaca, 36(3)(1986), 297–312.
• Njamcul, A., Pavlovi´c, A., On closure compatibility of ideal topological spaces and idempotency of the local closure function, Periodica Mathematica Hungarica, 84(2022), 221–234.
• Noorie, N.S., Goyal, N., On S 212 mod I spaces and θI-closed sets, International Journal of Mathematics Trends and Technology, 52(4)(2017), 226–228.
• Tunç, A.N., Özen Yıldırım, S., A study on further properties of local closure functions, 7th International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM 2020), (2020), 123–123.
• Tunç, A.N.,Özen Yıldırım, S., New sets obtained by local closure functions, Annals of Pure and Applied Mathematical Sciences, 1(1)(2021), 50–59.
• Tunç, A.N., Özen Yıldırım, S., ΨΓ − C sets in ideal topological spaces, Turk. J. Math. Comput. Sci., 15(1)(2023), 27–34.
• Vaidyanathaswamy, R., The localisation theory in set-topology, Proc. Indian Acad. Sci., Sect. A., 20(1944), 51–61.
• Veliˇcko, N.V., H-closed topological spaces, Amer. Math. Soc. Transl., 78(2)(1968), 102–118.
• Yalaz, F., Keskin Kaymakçı, A., New set types, decomposition of continuity and Γ−I−continuity via local closure function, Advanced Studies: Euro-Tbilisi Mathematical Journal, 16(3)(2023), 1–14.