Decomposition of gω-continuity Idealization


  • K. Meena
  • R. Premkumar
  • O. Ravi


In this paper we introduce the notions of g-I!-open sets, gp-I!-
open sets, gs-I!-open sets, g!t-I-sets, g! -I-sets and g!S-I-sets in ideal topological spaces and investigate some of their properties. Using these notions we obtain decompositions of g!-continuity.


[1] Acikgoz, A., Noiri, T. and Yuksel, S. On alfa-I-continuous and alfa-I-open functions. Acta Math. Hungar., 105(1-2)(2004), 27-37.

[2] Al-Omari, A. and Noorani, M. S. M. Regular generalized !-closed sets. Intern. J. Math. Math. Sci., Volume 2007, Article ID 16292, 11 pages, doi: 10.1155/2007/16292.

[3] Hdeib, H. Z. !-closed mappings. Revista Colomb. De Matem., 16(1-2)(1982), 65-78.

[4] Khalid, Y. Al-Zoubi. On generalized !-closed sets. Intern. J. Math. Math. Sci., 13(2005), 2011-2021.

[5] Kuratowski, K. Topology, Vol. 1, Academic Press, New York 1966.

[6] Levine, N. Semi-open sets and semi-continuity in topological spaces. Amer. Math. Monthly, 70(1963), 36-41.

[7] Levine, N. A decomposition of continuity in topological spaces. Amer. Math. Monthly, 68(1961), 44-46.

[8] Mashhour, A. S., Abd El-Monsef, M. E. and El-Deeb, S. N. On precontinuous and weak precontinuous mappings. Proc. Math. Phys. Soc. Egypt, 53(1982), 47-53.

[9] Njastad, O. On some classes of nearly open sets. Pacific J. Math., 15(1965), 961-970.

[10] Noiri, T., Al-Omari, A. and Noorani, M. S. M.Weak forms of !-open sets and decompositions of continuity, Eur. J. Pure Appl. Math., 2(1)(2009), 73-84.

[11] Noiri, T., Rajamani, M. and Inthumathi, V. On decompositions of g-continuity via idealization. Bull. Cal. Math. Soc., 99(4)(2007), 415-424.

[12] Ravi, O., Rajasekaran, I., Satheesh Kanna, S. and Paranjothi, M. New generalized classes of taw/omega!. Eur. J. Pure Appl. Math., 9(2)(2016), 152-164.

[13] Ravi, O., Murugesan, S. and Paranjothi, M. ⋆!-operfect sets and alfa-⋆!-closed sets. South Asian J. Math., 6(6)(2016), 300-314.

[14] Ravi, O., Sekar, P. and Vidhyalakshmi, K. New generalized classes of taw/omega in ideal spaces, South Asian J. Math., 6(3)(2016), 126-139.

[15] Ravi, O., Sekar, P. and Vidhyalakshmi, K. !-topology and ⋆-topology. Bull. Inter. Math. Virtual Inst., 7(1)(2017), 139-151.

[16] Rose, D. On Levine's decomposition of continuity. Canad. Math. Bull., 21(1978), 477-481.

[17] Sundaram, P. and Rajamani, M. On decompositions of generalized continuous maps in topological spaces, Acta Ciencia Indica, 26(2)(2000), 101-104.

[18] Tong, J. A decomposition of continuity. Acta Math. Hungar., 48(1986), 11-15.

[19] Umamaheswari, R., Nethaji, O. and Ravi, O. g!-continuity and its decompositions. South Asian J. Math., 7(1)(2017), 53-63.

[20] Vaidyanathaswamy, R. The localization theory in set topology. Proc. Indian Acad. Sci., Sect A, 20(1944), 51-61.

[21] Willard, S. General Topology, Addison-Wesley, Reading, Mass, USA, 1970.