Generalized Pre α-Closed Sets in Topology

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

Praveen Hanamantrao Patil Prakashgouda Guranagouda Patil

https://izlik.org/JA78SP52PR

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.

Keywords

Closed sets , gp®-closed sets , gp®-open 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.