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Generalized Pre α-Closed Sets in Topology

Year 2018, Issue: 20, 48 - 56, 26.01.2018

Abstract

In this paper, a new class of sets called generalized pre α-closed sets are introduced and studied in topological spaces, which are properly placed between the class of pre closed and the class of generalized star pre closed (g*p-closed) sets.

References

  • [1] D. Andrijevic, Semi-preopen sets, Mat. Vesnik, 38 (1) (1986) 24-32.
  • [2] S. P. Arya and T. M. Nour, Charactrezations of s-Normal spaces, Indian Jl.Pure and Appld.Math., 21 (1990) 717-719.
  • [3] S. S. Benchalli, P. G. Patil and T. D. Rayanagoudar, !®-closed sets in topo- logical spaces, The Global Jl. Appl. Maths and Math Sciences, 2 (2009) 53-63.
  • [4] P. Bhattacharya and B. K. Lahiri, Semi-generalized closed sets in topology, The Indian. Jl. Math, 29 (3) (1987) 375-382.
  • [5] J. Dontchev, On generalizing semi-preopen sets, Mem. Fac. Sci., Kochi Univ., Ser. A. Math, 16 (1995) 35-48.
  • [6] W. Dunham and N. Levine, Further results on generalized closed sets in topol- ogy, Kyungpook Math. Jl, 20 (1980) 169-175.
  • [7] Y. Gnanambal, On Generalized pre-regular closed sets in topological spaces, Indian Jl. Pure. Appl. Math. 28 (3) (1997) 351-360.
  • [8] 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, 3 (2012) 55-59.
  • [9] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963) 36-41.
  • [10] N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19 (2)(1970) 89-96.
  • [11] H. Maki, Generalized ¤-sets and associated closure operator, The Special Issue in Commemoration of Prof. Kazusada IKEDA's Retirement, (1986) 139-146.
  • [12] H. Maki, R. Devi and K. Balachandran, Generalized ®-closed sets in topology, Bull. Fukuoka Uni. Ed. Part III, 42 (1993) 13-21.
  • [13] H. Maki, J.Umehare and T.Nori, Every topological space is Pre-T1=2, Mem.Fac.Soc.Kochi Univ.Math.,17(1996) 32-42.
  • [14] A. S. Mashhour, M. E. Abd El-Monesf and S. N. El-Deeb, On pre-continuous and weak pre continuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982) 47-53.
  • [15] A. S. Mashhour, M. E. Abd El-Monesf and S. N. El-Deeb, ®-continuous and ®-open mappings, Acta Math Hung. 41 (1983) 213-218.
  • [16] O. Njasted, On some classes of nearly open sets, Paci¯c Jl. Math, 15 (1965) 961-970.
  • [17] M. Stone, Absolutely FG spaces, Proc. Amer. Math. Soc., 80 (1980) 515-520.
  • [18] P. Sundaram and M. Sheik John, On !-closed sets in topology, Acta. Ciencia Indica, 4 (2000) 389-392.
  • [19] M. K. R. S. Veerakumar, g*pre-closed sets, Acta. Ciencia Indica, 28 (2002) 51-60.
Year 2018, Issue: 20, 48 - 56, 26.01.2018

Abstract

References

  • [1] D. Andrijevic, Semi-preopen sets, Mat. Vesnik, 38 (1) (1986) 24-32.
  • [2] S. P. Arya and T. M. Nour, Charactrezations of s-Normal spaces, Indian Jl.Pure and Appld.Math., 21 (1990) 717-719.
  • [3] S. S. Benchalli, P. G. Patil and T. D. Rayanagoudar, !®-closed sets in topo- logical spaces, The Global Jl. Appl. Maths and Math Sciences, 2 (2009) 53-63.
  • [4] P. Bhattacharya and B. K. Lahiri, Semi-generalized closed sets in topology, The Indian. Jl. Math, 29 (3) (1987) 375-382.
  • [5] J. Dontchev, On generalizing semi-preopen sets, Mem. Fac. Sci., Kochi Univ., Ser. A. Math, 16 (1995) 35-48.
  • [6] W. Dunham and N. Levine, Further results on generalized closed sets in topol- ogy, Kyungpook Math. Jl, 20 (1980) 169-175.
  • [7] Y. Gnanambal, On Generalized pre-regular closed sets in topological spaces, Indian Jl. Pure. Appl. Math. 28 (3) (1997) 351-360.
  • [8] 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, 3 (2012) 55-59.
  • [9] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963) 36-41.
  • [10] N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19 (2)(1970) 89-96.
  • [11] H. Maki, Generalized ¤-sets and associated closure operator, The Special Issue in Commemoration of Prof. Kazusada IKEDA's Retirement, (1986) 139-146.
  • [12] H. Maki, R. Devi and K. Balachandran, Generalized ®-closed sets in topology, Bull. Fukuoka Uni. Ed. Part III, 42 (1993) 13-21.
  • [13] H. Maki, J.Umehare and T.Nori, Every topological space is Pre-T1=2, Mem.Fac.Soc.Kochi Univ.Math.,17(1996) 32-42.
  • [14] A. S. Mashhour, M. E. Abd El-Monesf and S. N. El-Deeb, On pre-continuous and weak pre continuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982) 47-53.
  • [15] A. S. Mashhour, M. E. Abd El-Monesf and S. N. El-Deeb, ®-continuous and ®-open mappings, Acta Math Hung. 41 (1983) 213-218.
  • [16] O. Njasted, On some classes of nearly open sets, Paci¯c Jl. Math, 15 (1965) 961-970.
  • [17] M. Stone, Absolutely FG spaces, Proc. Amer. Math. Soc., 80 (1980) 515-520.
  • [18] P. Sundaram and M. Sheik John, On !-closed sets in topology, Acta. Ciencia Indica, 4 (2000) 389-392.
  • [19] M. K. R. S. Veerakumar, g*pre-closed sets, Acta. Ciencia Indica, 28 (2002) 51-60.
There are 19 citations in total.

Details

Journal Section Research Article
Authors

Praveen Hanamantrao Patil This is me

Prakashgouda Guranagouda Patil

Publication Date January 26, 2018
Submission Date December 7, 2017
Published in Issue Year 2018 Issue: 20

Cite

APA Patil, P. H., & Patil, P. G. (2018). Generalized Pre α-Closed Sets in Topology. Journal of New Theory(20), 48-56.
AMA Patil PH, Patil PG. Generalized Pre α-Closed Sets in Topology. JNT. January 2018;(20):48-56.
Chicago Patil, Praveen Hanamantrao, and Prakashgouda Guranagouda Patil. “Generalized Pre Α-Closed Sets in Topology”. Journal of New Theory, no. 20 (January 2018): 48-56.
EndNote Patil PH, Patil PG (January 1, 2018) Generalized Pre α-Closed Sets in Topology. Journal of New Theory 20 48–56.
IEEE P. H. Patil and P. G. Patil, “Generalized Pre α-Closed Sets in Topology”, JNT, no. 20, pp. 48–56, January 2018.
ISNAD Patil, Praveen Hanamantrao - Patil, Prakashgouda Guranagouda. “Generalized Pre Α-Closed Sets in Topology”. Journal of New Theory 20 (January 2018), 48-56.
JAMA Patil PH, Patil PG. Generalized Pre α-Closed Sets in Topology. JNT. 2018;:48–56.
MLA Patil, Praveen Hanamantrao and Prakashgouda Guranagouda Patil. “Generalized Pre Α-Closed Sets in Topology”. Journal of New Theory, no. 20, 2018, pp. 48-56.
Vancouver Patil PH, Patil PG. Generalized Pre α-Closed Sets in Topology. JNT. 2018(20):48-56.


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