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Generalized Star ωα-Closed Sets in Topological Spaces

Year 2015, Volume: 4 Issue: 9 , 37 - 45 , 01.09.2015
https://izlik.org/JA98WJ84XK

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
https://izlik.org/JA98WJ84XK

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
Authors

P.g. Patil

Ss Benchalli This is me

Pallavi Mirajakar

Publication Date September 1, 2015
IZ https://izlik.org/JA98WJ84XK
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. https://izlik.org/JA98WJ84XK
AMA 1.Patil P, Benchalli S, Mirajakar P. Generalized Star ωα-Closed Sets in Topological Spaces. JNRS. 2015;4(9):37-45. https://izlik.org/JA98WJ84XK
Chicago Patil, P.g., Ss Benchalli, and Pallavi Mirajakar. 2015. “Generalized Star ωα-Closed Sets in Topological Spaces”. Journal of New Results in Science 4 (9): 37-45. https://izlik.org/JA98WJ84XK.
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 [1]P. Patil, S. Benchalli, and P. Mirajakar, “Generalized Star ωα-Closed Sets in Topological Spaces”, JNRS, vol. 4, no. 9, pp. 37–45, Sept. 2015, [Online]. Available: https://izlik.org/JA98WJ84XK
ISNAD Patil, P.g. - Benchalli, Ss - Mirajakar, Pallavi. “Generalized Star ωα-Closed Sets in Topological Spaces”. Journal of New Results in Science 4/9 (September 1, 2015): 37-45. https://izlik.org/JA98WJ84XK.
JAMA 1.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, Sept. 2015, pp. 37-45, https://izlik.org/JA98WJ84XK.
Vancouver 1.P.g. Patil, Ss Benchalli, Pallavi Mirajakar. Generalized Star ωα-Closed Sets in Topological Spaces. JNRS [Internet]. 2015 Sep. 1;4(9):37-45. Available from: https://izlik.org/JA98WJ84XK

 

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