Between *-Closed Sets and Iw-Closed Sets
Year 2013,
Volume: 2 Issue: 3, 87 - 97, 01.03.2013
O. Ravi
J.antony Rex Rodrigo
Abstract
–closed sets ( Iω-closed sets ) and further properties of Iˆg-closedsets are investigated. In this paper, we introduce the notion ofImω-closed sets and obtain the unified characterizations for certain families of subsets between -closed sets and Iω-closed setsin an ideal topological space
References
- S. P. Arya and T. M. Noiri, Characterizations of s-normal spaces, Indian J. Pure Appl. Math., 21(1990), 717-719.
- P. Bhattacharyya and B. K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math., 29(3)(1987), 375-382.
- S. G. Crossley and S. K. Hildebrand, Semi-closure, Texas J. Sci., 22(1971), 99-112. [4] J. Dontchev, M. Ganster and T. Noiri, Unified operation approach of generalized closed sets via topological ideals, Math. Japon., 49 (1999), 395-401.
- J. Dontchev, On generalizing semi-preopen sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 16(1995), 35-48.
- T. R. Hamlett, D. Rose and D. Jankovic, Paracompactness with respect to an ideal, Internat. J. Math. Math. Sci., 20(1997), 433-442.
- S. Jafari, T. Noiri, N. Rajesh and M. L. Thivagar, Another generalization of closed sets, Kochi J. Math., 3(2008), 25-38.
- 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, Generalized closed sets in topology, Rend. Circ. Mat. Palermo., 19(2)(1970), 89-96.
- N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
- H. Maki, K. C. Rao and A. Nagoor Gani, On generalizing semi-open and preopen sets, Pure Appl. Math. Sci., 49(1999), 17-29.
- 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.
- W. K. Min, m-semiopen sets and M-semicontinuous functions on spaces with min- imal structures, Honam Mathematical Journal, 31(2)(2009), 239-245.
- M. Navaneethakrishnan and J. Paulraj Joseph, g-closed sets in ideal topological spaces, Acta Math Hungar., 119(4)(2008), 365-371.
- O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961- 970.
- T. Noiri and V. Popa, Between -closed sets and Ig-closed sets in ideal topological spaces, Rend. Circ. Mat. Palermo, 59(2010), 251-260.
- O. B. Ozbakir and E. D. Yildirim, On some closed sets in ideal minimal spaces, Acta Math. Hungar., 125(3)(2009), 227-235.
- V. Popa and T. Noiri, On M-continuous functions, Anal. Univ. ”Dunarea de Jos” Galati, Ser. Mat. Fiz. Mec. Teor., (2), 18(23)(2000), 31-41.
- N. Rajesh, M. Lellis Thivagar, P. Sundaram and Zbigniew Duszynski, ˜g-semi-closed sets in topological spaces, Mathematica Pannonica, 18(1)(2007), 51-61.
- O. Ravi, J. Antony Rex Rodrigo and A. Naliniramalatha, ˆg-closed sets in ideal topological spaces, Methods of Functional Analysis and Topology, 17(3)(2011), 274-280.
- O. Ravi, J. Antony Rex Rodrigo and A. Naliniramalatha, Between closed sets and ω-closed sets, submitted.
- O. Ravi, R. G. Balamurugan, J. Antony Rex Rodrigo and K. Vijayalakshmi, A unified theory for modifications of ˆg-closed sets, International Journal of Advances in Pure and Applied Mathematics, 1(1)(2011), 53-67.
- O. Ravi, J. Antony Rex Rodrigo, S. Tharmar and K. Vijayalakshmi, Between closed sets and g-closed sets, Fasciculi Mathematici, 49(2012), 127-136.
- M. Sheik John, A study on generalizations of closed sets and continuous maps in topological and bitopological spaces, Ph. D Thesis, Bharathiar University, Coim- batore, 2002.
- R. Vaidyanathaswamy, Set Topology, Chelsea Publishing Company (1946).
- M. K. R. S. Veerakumar, ˆg-closed sets in topological spaces, Bull. Allahabad Math. Soc., 18(2003), 99-112.
- M. K. R. S. Veerakumar,#g-semi-closed sets in topological spaces, Antarctica J. Math., 2(2)(2005), 201-222.
- M. K. R. S. Veerakumar, Between g -closed sets and g-closed sets, Antartica J. Math., 3(1)(2006), 43-65.
- M. K. R. S. Veerakumar, Semi-pre-generalized closed sets, Mem. Fac. Sci. Kochi Univ. (Japan) Ser. A. Math., 20(1999), 33-46.
Year 2013,
Volume: 2 Issue: 3, 87 - 97, 01.03.2013
O. Ravi
J.antony Rex Rodrigo
References
- S. P. Arya and T. M. Noiri, Characterizations of s-normal spaces, Indian J. Pure Appl. Math., 21(1990), 717-719.
- P. Bhattacharyya and B. K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math., 29(3)(1987), 375-382.
- S. G. Crossley and S. K. Hildebrand, Semi-closure, Texas J. Sci., 22(1971), 99-112. [4] J. Dontchev, M. Ganster and T. Noiri, Unified operation approach of generalized closed sets via topological ideals, Math. Japon., 49 (1999), 395-401.
- J. Dontchev, On generalizing semi-preopen sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 16(1995), 35-48.
- T. R. Hamlett, D. Rose and D. Jankovic, Paracompactness with respect to an ideal, Internat. J. Math. Math. Sci., 20(1997), 433-442.
- S. Jafari, T. Noiri, N. Rajesh and M. L. Thivagar, Another generalization of closed sets, Kochi J. Math., 3(2008), 25-38.
- 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, Generalized closed sets in topology, Rend. Circ. Mat. Palermo., 19(2)(1970), 89-96.
- N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
- H. Maki, K. C. Rao and A. Nagoor Gani, On generalizing semi-open and preopen sets, Pure Appl. Math. Sci., 49(1999), 17-29.
- 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.
- W. K. Min, m-semiopen sets and M-semicontinuous functions on spaces with min- imal structures, Honam Mathematical Journal, 31(2)(2009), 239-245.
- M. Navaneethakrishnan and J. Paulraj Joseph, g-closed sets in ideal topological spaces, Acta Math Hungar., 119(4)(2008), 365-371.
- O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961- 970.
- T. Noiri and V. Popa, Between -closed sets and Ig-closed sets in ideal topological spaces, Rend. Circ. Mat. Palermo, 59(2010), 251-260.
- O. B. Ozbakir and E. D. Yildirim, On some closed sets in ideal minimal spaces, Acta Math. Hungar., 125(3)(2009), 227-235.
- V. Popa and T. Noiri, On M-continuous functions, Anal. Univ. ”Dunarea de Jos” Galati, Ser. Mat. Fiz. Mec. Teor., (2), 18(23)(2000), 31-41.
- N. Rajesh, M. Lellis Thivagar, P. Sundaram and Zbigniew Duszynski, ˜g-semi-closed sets in topological spaces, Mathematica Pannonica, 18(1)(2007), 51-61.
- O. Ravi, J. Antony Rex Rodrigo and A. Naliniramalatha, ˆg-closed sets in ideal topological spaces, Methods of Functional Analysis and Topology, 17(3)(2011), 274-280.
- O. Ravi, J. Antony Rex Rodrigo and A. Naliniramalatha, Between closed sets and ω-closed sets, submitted.
- O. Ravi, R. G. Balamurugan, J. Antony Rex Rodrigo and K. Vijayalakshmi, A unified theory for modifications of ˆg-closed sets, International Journal of Advances in Pure and Applied Mathematics, 1(1)(2011), 53-67.
- O. Ravi, J. Antony Rex Rodrigo, S. Tharmar and K. Vijayalakshmi, Between closed sets and g-closed sets, Fasciculi Mathematici, 49(2012), 127-136.
- M. Sheik John, A study on generalizations of closed sets and continuous maps in topological and bitopological spaces, Ph. D Thesis, Bharathiar University, Coim- batore, 2002.
- R. Vaidyanathaswamy, Set Topology, Chelsea Publishing Company (1946).
- M. K. R. S. Veerakumar, ˆg-closed sets in topological spaces, Bull. Allahabad Math. Soc., 18(2003), 99-112.
- M. K. R. S. Veerakumar,#g-semi-closed sets in topological spaces, Antarctica J. Math., 2(2)(2005), 201-222.
- M. K. R. S. Veerakumar, Between g -closed sets and g-closed sets, Antartica J. Math., 3(1)(2006), 43-65.
- M. K. R. S. Veerakumar, Semi-pre-generalized closed sets, Mem. Fac. Sci. Kochi Univ. (Japan) Ser. A. Math., 20(1999), 33-46.