Volume 27 • Issue 2 • PP: 132-143 • 2026
I_g^*-Continues and I_g^*-irresoluteness
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© 2026 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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In this paper, I_g^*- closed sets, and I_g^*- open are used to investigate and define a new class of functions is said to be I_g^*-Continues functions, I_g^*-irresolute functions in ideal topological space topological spaces. Morover, I introduce I_g^*- compact spaces and I_g^*-connected spaces, and maximal I_g^*-closed sets. I obtain their characterizations and study their basic properties.
Keywords
References
[1] M. E. Abd El-Monsef, E. F. Lashien, and A. A. Nasef, Some topological operations via ideals, Kyungpook Matheatical Journal,32.2.,pp 273–284, 1992.
[2] Al-Omeri, W., Abu-Saleem, M., I˚g-closed sets via ideal topological spaces.Missouri Journal of Mathematical Sciences, 31(2). pp. 174–191, 2019.
[3] F. G. Arenas, J. Dontchev, and M. L. Puertas, Idealization of some weak separation axioms, Acta Math. Hungar, 89.1 –2. pp. 47–53, 2000.
[4] S. P. Arya and T. M. Nour, Characterizations of s-normal spaces, Indian Journal of Pure and Applied Mathematics, 21.8. pp. 717–719, 1990.
[5] V. R. Devi, D. Sivaraj, and T. T. Chelvam, Codense and completely codense ideals, Acta Mathematica Hungarica,108.pp. 197–205, 2005.
[6] J. Dontchev, On generalizing semi-preopen sets, Memoirs of the Faculty of Science Kochi University Series A Mathematics, 16.pp. 35–48,1995.
[7] Y. Gnanambal, On generalized preregular closed sets in topological spaces, Indian Journal of Pure and Applied Mathematics, 28.3.pp. 351–360,1997.
[8] E. Hatir and S. Jafari, On weakly semi-i-open sets and another decomposition of continuity via ideals, Sarajevo J. Math., 2.no. 14.pp 107–114, 2006.
[9] D. Jankovic and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97.pp. 295–310, 1990.
[10] Ara´ujo, R. F. D. A., Ferreira, F. S., and Almeida, L. C. F., ”On the ideal topologies generated by filters,” Topology and its Applications, vol. 300, pp. 1–10, 2022.
[11] A. Kar and P. Bhattacharyya, Weakly semi-continuous functions, J. Indian Acad. Math., 8.pp. 83–93, 1986.
[12] E. D. Khalimsky, Applications of connected ordered topological spaces in topology, Conference of Math. Department of Povolsia, 1970.
[13] Wu, J. X., ”Generalized closed sets and their applications in topology,” Topology and its Applications, vol. 313, pp. 1–15, 2022.
[14] N. Levine, Generalized closed sets in topology, Rendiconti del Circolo Matematica di Palermo Series 2, 19.pp. 89–96, 1970.
[15] H. Maki, R. Devi, and K. Balachandran, Associated topologies of generalized α-closed sets and α-generalized closed sets, Memoirs of the Faculty of Science Kochi University Series A Mathematics, 15.pp. 51–63, 1994.
[16] A. S. Mashhour, M. E. El-Monsef, and S. N. El-Deeb, On precontinuous and weak precontinuous functions, Proc. Math. Phys. Soc. Egypt, 53.pp.47–53, 1982.
[17] M. N. Mukherjee, R. Bishwambhar, and R. Sen, On extension of topological spaces in terms of ideals, Topology and its Appl.,154.pp. 3167–3172, 2007.
[18] M. Murugalingam, A study of semi generalized topology, Ph.D. Thesis, Manonmaniam Sundaranar University Tirunelveli Tamil Nadu India, 2005.
[19] A. A. Nasef and R. A. Mahmoud, Some applications via fuzzy ideals, Chaos, Solitons and Fractals,13.pp. 825–831,2002.
[20] R. L. Newcomb, Topologies which are compact modulo an ideal, Ph.D. Dissertation. University of California - Santa Barbara, 1967.
[21] T. Noiri and V. Popa, Between ˚-closed and I-g-closed sets in ideal topological spaces, Rendiconti del Circolo Matematico di Palermo,59.pp. 251–260, 2010.
[22] N. Palaniappan and K. C. Rao, Regular generalized closed sets, Kyungpook Mathematics Journal,33.pp. 211–2191993..
[23] D. Ranˇc, In compactness modulo an ideal, Soviet Mathematics, Doklady, 13.1. pp. 193–197,1973.
[24] O. Ravi and S. Tharmar, ˚g-closed sets in ideal topological spaces, Jordan Journal of Mathematics and Statistics,6.1.pp. 1–13, 2013.
[25] K. Kuratowski, Topology, Vol. I. NewYork: Academic Press (1966).
[26] R. Vaidyanathaswamy, The localization theory in set-topology, Proceedings of the Indian Academy of Science, 20.pp. 51–60, 1945.
[27] S. Y¨uksel, A. Ac¸ikg¨oz, and T. Noiri, On α-I-continuous functions, Turk. J. Math., 29.pp. 39–51, 2005.
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