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Between *-Closed Sets and Iw-Closed Sets

Year 2013, Volume: 2 Issue: 3, 87 - 97, 01.03.2013

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

Abstract

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.
There are 29 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

O. Ravi This is me

J.antony Rex Rodrigo This is me

Publication Date March 1, 2013
Published in Issue Year 2013 Volume: 2 Issue: 3

Cite

APA Ravi, O., & Rodrigo, J. R. (2013). Between *-Closed Sets and Iw-Closed Sets. Journal of New Results in Science, 2(3), 87-97.
AMA Ravi O, Rodrigo JR. Between *-Closed Sets and Iw-Closed Sets. JNRS. March 2013;2(3):87-97.
Chicago Ravi, O., and J.antony Rex Rodrigo. “Between *-Closed Sets and Iw-Closed Sets”. Journal of New Results in Science 2, no. 3 (March 2013): 87-97.
EndNote Ravi O, Rodrigo JR (March 1, 2013) Between *-Closed Sets and Iw-Closed Sets. Journal of New Results in Science 2 3 87–97.
IEEE O. Ravi and J. R. Rodrigo, “Between *-Closed Sets and Iw-Closed Sets”, JNRS, vol. 2, no. 3, pp. 87–97, 2013.
ISNAD Ravi, O. - Rodrigo, J.antony Rex. “Between *-Closed Sets and Iw-Closed Sets”. Journal of New Results in Science 2/3 (March 2013), 87-97.
JAMA Ravi O, Rodrigo JR. Between *-Closed Sets and Iw-Closed Sets. JNRS. 2013;2:87–97.
MLA Ravi, O. and J.antony Rex Rodrigo. “Between *-Closed Sets and Iw-Closed Sets”. Journal of New Results in Science, vol. 2, no. 3, 2013, pp. 87-97.
Vancouver Ravi O, Rodrigo JR. Between *-Closed Sets and Iw-Closed Sets. JNRS. 2013;2(3):87-9.


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