Ig -⋆-closed Sets
Keywords:
⋆-g-closed set, Ig-⋆-closed set, I-compact space
Abstract
The notion of I g-⋆-closed sets is introduced in ideal topological spaces. Characterizations and properties of Ig-⋆-closed sets and I g-⋆-open sets are given. A characterization of normal spaces is given in terms of Ig-⋆-open sets. Also, it is established that an I g-⋆-closed subset of an I-compact space is I-compact.
References
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J.Dontchev, M.Ganster and D.Rose, Ideal resolvability, Topology and its Applications, 93(1999), 1-16.
T.R.Hamlett and D.Jankovic, Compactness with respect to an ideal, Boll. U. M. I., 7(4-B)(1990), 849-861.
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D.Mandal and M.N.Mukherjee, Certain new classes of generalized closed sets and their applications in ideal topological spaces, Filomat., 29(5)(2015), 1113-1120.
A.S.Mashhour, M.E.Abd El-Monsef and S.N.El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47-53.
M.Navaneethakrishnan and J.Paulraj Joseph, g-closed sets in ideal topological spaces, Acta Math. Hungar., 119(4)(2008), 365-371.
R.L.Newcomb, Topologies which are compact modulo an ideal, Ph.D. Dissertation, Univ. of Cal. at Santa Barbara, (1967).
O.Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970.
V.Renuka Devi, D.Sivaraj and T.Tamizh Chelvam, Codense and Completely codense ideals, Acta Math. Hungar., 108(2005), 197-205.
R.Vaidyanathaswamy, Set Topology, Chelsea Publishing Company, (1946).
J.Dontchev, M.Ganster and D.Rose, Ideal resolvability, Topology and its Applications, 93(1999), 1-16.
T.R.Hamlett and D.Jankovic, Compactness with respect to an ideal, Boll. U. M. I., 7(4-B)(1990), 849-861.
E.Hayashi, Topologies defined by local properties, Math. Ann., 156(1964), 205-215.
V.Inthumathi, S.Krishnaprakash and M.Rajamani, Strongly-I-Locally closed sets and decompositions of ⋆-continuity, Acta Math. Hungar., 130(4)(2011), 358-362.
D.Jankovic and T.R.Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(4)(1990), 295-310.
A.Keskin, S.Yuksel and T.Noiri, Decompositions of I-continuity and continuity, Commun. Fac. Sci. Univ. Ank. Series A, 53(2004), 67-75.
K.Kuratowski, Topology, Vol. I, Academic Press, New York, (1966).
N.Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
N.Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(2)(1970), 89-96.
D.Mandal and M.N.Mukherjee, Certain new classes of generalized closed sets and their applications in ideal topological spaces, Filomat., 29(5)(2015), 1113-1120.
A.S.Mashhour, M.E.Abd El-Monsef and S.N.El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47-53.
M.Navaneethakrishnan and J.Paulraj Joseph, g-closed sets in ideal topological spaces, Acta Math. Hungar., 119(4)(2008), 365-371.
R.L.Newcomb, Topologies which are compact modulo an ideal, Ph.D. Dissertation, Univ. of Cal. at Santa Barbara, (1967).
O.Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970.
V.Renuka Devi, D.Sivaraj and T.Tamizh Chelvam, Codense and Completely codense ideals, Acta Math. Hungar., 108(2005), 197-205.
R.Vaidyanathaswamy, Set Topology, Chelsea Publishing Company, (1946).
How to Cite
K.Meena, O.Nethaji, R.Premkumar, & O.Ravi. (2017). Ig -⋆-closed Sets. International Journal of Current Research in Science and Technology, 3(1), 37-45. Retrieved from https://crst.gfer.org/index.php/crst/article/view/81
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