Mildly Ig-ω-Closed Sets
Abstract
In this paper, another generalized class of ⋆ called mildly Ig-!-closed sets is introduced and the notion of mildly Ig-!-open sets in ideal topological spaces is introduced and studied. The relationships of mildly Ig-!-closed sets with various other sets are investigated.
References
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[10] D. Jankovic and T. R. Hamlett. New topologies from old via ideals, Amer. Math. Monthly, 97(4)(1990), 295-310.
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[13] N. Levine. Generalized closed sets in topology, Rend. Cir. Math. Palermo, (2), 19(1970), 89-96.
[14] M. Navaneethakrishnan and J. Paulraj Joseph. g-closed sets in ideal topological spaces, Acta Math. Hungar., 119(4)(2008), 365-371.
[15] T. Noiri, A. Al-Omari and M. S. M. Noorani. Weak forms of !-open sets and decompositions of continuity, Eur. J. Pure Appl. Math., 2(1)(2009), 73-84.
[16] J. K. Park and J. H. Park. Mildly generalized closed sets, almost normal and mildly normal spaces, Chaos, Solitons and Fractals, 20(2004), 1103-1111.
[17] P. Sundaram and N. Nagaveni. On weakly generalized continuous maps, weakly generalized closed maps and weakly generalized irresolute maps in topological spaces, Far East J. Math. Sci., 6(6)(1998), 903-1012.
[18] P. Sundaram and A. Pushpalatha. Strongly generalized closed sets in topological spaces, Far East J. Math. Sci., 3(4)(2001), 563-575.
[19] R. Vaidyanathaswamy. Set Topology, Chelsea Publishing Company, 1946.
[20] S. Willard. General Topology, Addison-Wesley, Reading, Mass, USA, 1970.
[2] A. Acikgoz and S. Yuksel. Some new sets and decompositions of AI-R-continuity, alfa-I-continuity, continuity via idealization, Acta Math. Hungar., 114(1-2)(2007), 79-89.
[3] A. Al-Omari and M. S. M. Noorani. Contra-!-continuous and Almost contra-!-continuous, Intern. J. Math. Math. Sci., Vol. 2007, Artical ID 40469, 13 Pages. doi:10.1155/2007/40469
[4] A. Al-Omari and M. S. M. Noorani. Regular generalized !-closed sets, Intern. J. Math. Math. Sci., Vol. 2007, Article ID 16292, 11 Pages, doi: 10.1155/2007/16292.
[5] K. Banumathi, R. Premkumar and O. Ravi, Ig-!-closed sets, Submitted.
[6] J. Dontchev, M. Ganster and T. Noiri. Unified operation approach of generalized closed sets via topological ideals, Math. Japonica, 49(1999), 395-401.
[7] E. Ekici. On ACI-sets, BCI-sets, ⋆
I -open sets and decompositions of continuity in ideal
topological spaces, Creat. Math. Inform., 20(2011), 47-54.
[8] E. Ekici and S. Ozen. A generalized class of beta⋆ in ideal spaces, Filomat, 27(4)(2013), 529-535.
[9] H. Z. Hdeib. !-closed mappings, Revista Colomb. De Matem., 16(1-2)(1982), 65-78.
[10] D. Jankovic and T. R. Hamlett. New topologies from old via ideals, Amer. Math. Monthly, 97(4)(1990), 295-310.
[11] Khalid Y. Al-Zoubi. On generalized !-closed sets, Intern. J. Math. Math. Sci., 13(2005), 2011-2021.
[12] K. Kuratowski. Topology, Vol. I, Academic Press, New York, 1966.
[13] N. Levine. Generalized closed sets in topology, Rend. Cir. Math. Palermo, (2), 19(1970), 89-96.
[14] M. Navaneethakrishnan and J. Paulraj Joseph. g-closed sets in ideal topological spaces, Acta Math. Hungar., 119(4)(2008), 365-371.
[15] T. Noiri, A. Al-Omari and M. S. M. Noorani. Weak forms of !-open sets and decompositions of continuity, Eur. J. Pure Appl. Math., 2(1)(2009), 73-84.
[16] J. K. Park and J. H. Park. Mildly generalized closed sets, almost normal and mildly normal spaces, Chaos, Solitons and Fractals, 20(2004), 1103-1111.
[17] P. Sundaram and N. Nagaveni. On weakly generalized continuous maps, weakly generalized closed maps and weakly generalized irresolute maps in topological spaces, Far East J. Math. Sci., 6(6)(1998), 903-1012.
[18] P. Sundaram and A. Pushpalatha. Strongly generalized closed sets in topological spaces, Far East J. Math. Sci., 3(4)(2001), 563-575.
[19] R. Vaidyanathaswamy. Set Topology, Chelsea Publishing Company, 1946.
[20] S. Willard. General Topology, Addison-Wesley, Reading, Mass, USA, 1970.
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2017-04-10
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