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Generalized Star ωα-Closed Sets in Topological Spaces

Year 2015, Volume: 4 Issue: 9, 37 - 45, 01.09.2015

Abstract

The aim of this paper is to introduce a new class of
closed sets called generalized star ωα-closed sets using ωα-closed
sets in topological spaces. This new class of sets lies between the
class of closed sets and the class of generalized ωα-closed sets.
Further some of their properties are investigated.

References

  • M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, β-Open Sets and β-Continuous Mappings, Bull. Fac. Sci. Assint Unie., 12, (1983),77-90.
  • D. Andrijivic, Semi pre Open Sets, Mat. Vesnic, 38(1), (1986), 24-32.
  • S. P. Arya and T. M. Nour, Characterizations of s-normal Spaces, Indian Jl. Pure Appl. Math., 21, (1990), 717-719.
  • S. S. Benchalli, P. G. Patil and T. D. Rayanagaudar, ωα-Closed Sets is Topological Spaces, The Global. Jl. Appl. Math. and Math. Sci., 2, (2009), 53-63.
  • S. S. Benchalli, P. G. Patil and P. M. Nalwad, Generalized ωα-Closed Sets in Topological Spaces, Jl. New Results in Science,, Vol 7, (2014), 7-19.
  • P. Bhattacharyya and B.K. Lahiri, Semi-generalized Closed Sets in Topology, Indian Jl. Math., 29, (1987), 376 - 382.
  • J. Dontchev, On Generalizing Semi-pre Open Sets, Mem. Fac. Kochi Univ. Math., 16, (1995), 35-48.
  • J. Dontchev, On Submaximal Spaces, Tankang Jl. Math., 26, (1995), 253-260.
  • Y. Gnanambal, On Generalized Pre-regular Closed Sets in Topological Spaces, Indian Jl. Pure Appl. Math., 28(3), (1997), 351-360.
  • S. Jafari, S. S. Benchalli, P. G. Patil and T. D. Rayanagoudar, Pre g∗-Closed Sets in Topological Spaces, Jl. of Advanced Studies in Topology, Vol 3, No.3, (2012), 55-59.
  • 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.
  • O. Njastad, On Some Classes of Nearly Open Sets, Pacific Jl. Math., 15, (1965), 961-970.
  • H. Maki, R. Devi and K. Balachandran, Generalized α-Closed Sets in Topology, Bull. Fukuoka Univ. Ed., Part III, 42, (1993), 13 -21.
  • H. Maki, R. Devi and K. Balachandran, Associated Topologies of Generalized α-Closed Sets and α-Generalized Closed Sets, Mem. Fac. Kochi Univ. Ser. A. Math., 15, (1994), 51-63.
  • H. Maki, J. Umehara and T. Noiri, Every Topological Space is Pre-T1/2, Mem.Fac. Sci. Kochi Univ. Math., 17, (1996), 33-42.
  • A. S. Mashhour, M. E. Abd El-Monsef and S. N. EL-Deeb, On Pre-Continuous and Weak Pre Continuous Mappings, Proc. Math and Phys. Soc. Egypt, 53, (1982), 47-53.
  • A. S. Mashour, M. E. Abd El-Monsef and S. N. El-Deeb, α-Open Mappings, Acta.Math. Hungar., 41, (1983), 213-218.
  • A. Pushpalatha, Studies on Generalizations of Mappings in Topological Spaces, Ph.D.Thesis, Bharathiar University, Coimbatore, (2000).
  • P. Sundaram and M. Sheik John, On ω-Closed Sets in Topology, Acta Ciencia Indica, 4, (2000), 389-392.
  • L. A. Steen and J. A. Seebach, Jr., Counter Examples in Topology, Springer Verlag, New York, 1978.
  • M. Stone, Application of the Theory of Boolean Rings to General Topology, Trans. Amer. Math. Soc. 41, (1937), 374-481.
  • M. K. R. S. Veera Kumar, g∗-preclosed Sets, Acta Ciencia Indica, 28(1), (2002), 51-60.
Year 2015, Volume: 4 Issue: 9, 37 - 45, 01.09.2015

Abstract

References

  • M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, β-Open Sets and β-Continuous Mappings, Bull. Fac. Sci. Assint Unie., 12, (1983),77-90.
  • D. Andrijivic, Semi pre Open Sets, Mat. Vesnic, 38(1), (1986), 24-32.
  • S. P. Arya and T. M. Nour, Characterizations of s-normal Spaces, Indian Jl. Pure Appl. Math., 21, (1990), 717-719.
  • S. S. Benchalli, P. G. Patil and T. D. Rayanagaudar, ωα-Closed Sets is Topological Spaces, The Global. Jl. Appl. Math. and Math. Sci., 2, (2009), 53-63.
  • S. S. Benchalli, P. G. Patil and P. M. Nalwad, Generalized ωα-Closed Sets in Topological Spaces, Jl. New Results in Science,, Vol 7, (2014), 7-19.
  • P. Bhattacharyya and B.K. Lahiri, Semi-generalized Closed Sets in Topology, Indian Jl. Math., 29, (1987), 376 - 382.
  • J. Dontchev, On Generalizing Semi-pre Open Sets, Mem. Fac. Kochi Univ. Math., 16, (1995), 35-48.
  • J. Dontchev, On Submaximal Spaces, Tankang Jl. Math., 26, (1995), 253-260.
  • Y. Gnanambal, On Generalized Pre-regular Closed Sets in Topological Spaces, Indian Jl. Pure Appl. Math., 28(3), (1997), 351-360.
  • S. Jafari, S. S. Benchalli, P. G. Patil and T. D. Rayanagoudar, Pre g∗-Closed Sets in Topological Spaces, Jl. of Advanced Studies in Topology, Vol 3, No.3, (2012), 55-59.
  • 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.
  • O. Njastad, On Some Classes of Nearly Open Sets, Pacific Jl. Math., 15, (1965), 961-970.
  • H. Maki, R. Devi and K. Balachandran, Generalized α-Closed Sets in Topology, Bull. Fukuoka Univ. Ed., Part III, 42, (1993), 13 -21.
  • H. Maki, R. Devi and K. Balachandran, Associated Topologies of Generalized α-Closed Sets and α-Generalized Closed Sets, Mem. Fac. Kochi Univ. Ser. A. Math., 15, (1994), 51-63.
  • H. Maki, J. Umehara and T. Noiri, Every Topological Space is Pre-T1/2, Mem.Fac. Sci. Kochi Univ. Math., 17, (1996), 33-42.
  • A. S. Mashhour, M. E. Abd El-Monsef and S. N. EL-Deeb, On Pre-Continuous and Weak Pre Continuous Mappings, Proc. Math and Phys. Soc. Egypt, 53, (1982), 47-53.
  • A. S. Mashour, M. E. Abd El-Monsef and S. N. El-Deeb, α-Open Mappings, Acta.Math. Hungar., 41, (1983), 213-218.
  • A. Pushpalatha, Studies on Generalizations of Mappings in Topological Spaces, Ph.D.Thesis, Bharathiar University, Coimbatore, (2000).
  • P. Sundaram and M. Sheik John, On ω-Closed Sets in Topology, Acta Ciencia Indica, 4, (2000), 389-392.
  • L. A. Steen and J. A. Seebach, Jr., Counter Examples in Topology, Springer Verlag, New York, 1978.
  • M. Stone, Application of the Theory of Boolean Rings to General Topology, Trans. Amer. Math. Soc. 41, (1937), 374-481.
  • M. K. R. S. Veera Kumar, g∗-preclosed Sets, Acta Ciencia Indica, 28(1), (2002), 51-60.
There are 23 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

P.g. Patil

Ss Benchalli This is me

Pallavi Mirajakar

Publication Date September 1, 2015
Published in Issue Year 2015 Volume: 4 Issue: 9

Cite

APA Patil, P., Benchalli, S., & Mirajakar, P. (2015). Generalized Star ωα-Closed Sets in Topological Spaces. Journal of New Results in Science, 4(9), 37-45.
AMA Patil P, Benchalli S, Mirajakar P. Generalized Star ωα-Closed Sets in Topological Spaces. JNRS. September 2015;4(9):37-45.
Chicago Patil, P.g., Ss Benchalli, and Pallavi Mirajakar. “Generalized Star ωα-Closed Sets in Topological Spaces”. Journal of New Results in Science 4, no. 9 (September 2015): 37-45.
EndNote Patil P, Benchalli S, Mirajakar P (September 1, 2015) Generalized Star ωα-Closed Sets in Topological Spaces. Journal of New Results in Science 4 9 37–45.
IEEE P. Patil, S. Benchalli, and P. Mirajakar, “Generalized Star ωα-Closed Sets in Topological Spaces”, JNRS, vol. 4, no. 9, pp. 37–45, 2015.
ISNAD Patil, P.g. et al. “Generalized Star ωα-Closed Sets in Topological Spaces”. Journal of New Results in Science 4/9 (September 2015), 37-45.
JAMA Patil P, Benchalli S, Mirajakar P. Generalized Star ωα-Closed Sets in Topological Spaces. JNRS. 2015;4:37–45.
MLA Patil, P.g. et al. “Generalized Star ωα-Closed Sets in Topological Spaces”. Journal of New Results in Science, vol. 4, no. 9, 2015, pp. 37-45.
Vancouver Patil P, Benchalli S, Mirajakar P. Generalized Star ωα-Closed Sets in Topological Spaces. JNRS. 2015;4(9):37-45.


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