Strongly g-⋆-closed Sets
Keywords:
Strongly g-⋆-closed set, strongly Ig-⋆-closed set, ⋆-g-closed set, I-compact space
Abstract
In this paper, the notion of strongly g-⋆-closed sets is introduced in ideal topological spaces. Characterizations and properties of strongly g-⋆-closed sets and strongly g-⋆-open sets are given. A characterization of normal spaces is given in terms of strongly g-⋆-open sets. Also it is established that a strongly 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.
E.Hayashi, Topologies defined by local properties, Math. Ann., 156(1964), 205-215.
D.Jankovic and T.R.Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(4)(1990), 295-310.
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.
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).
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 T.Noiri, Unified operation approach of generalized closed sets via topological ideals, Math. Japonica, 49(1999), 395-401.
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.
D.Jankovic and T.R.Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(4)(1990), 295-310.
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.
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).
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
R.Umamaheswari, R.Premkumar, & O.Ravi. (2017). Strongly g-⋆-closed Sets. International Journal of Current Research in Science and Technology, 3(2), 13-20. Retrieved from https://crst.gfer.org/index.php/crst/article/view/83
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