Strongly Ig-⋆-closed Sets
Keywords:
Strongly g-⋆-closed set, strongly Ig-⋆-closed set, ⋆-g-closed set, I-compact space
Abstract
In [14], the notion of strongly Ig-⋆-closed sets is introduced in ideal topological spaces. Characterizations and properties of strongly Ig-⋆-closed sets and strongly Ig-⋆-open sets are given. A characterization of normal spaces is given in terms of strongly Ig-⋆-open sets. Also, it is established that a strongly Ig-⋆-closed subset of an I-compact space is I-compact.
References
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K. Meena, M. Rajakalaivanan and O. Ravi, Mildly Ig-⋆-closed sets, International Journal of Current Research in Science and Technology, 2(12)(2016), 9-17.
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 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.
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 (2), 19(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.
K. Meena, M. Rajakalaivanan and O. Ravi, Mildly Ig-⋆-closed sets, International Journal of Current Research in Science and Technology, 2(12)(2016), 9-17.
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
V.P.Anuja, R.Premkumar, & O.Ravi. (2017). Strongly Ig-⋆-closed Sets. International Journal of Current Research in Science and Technology, 3(1), 1-9. Retrieved from https://crst.gfer.org/index.php/crst/article/view/78
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