Generalized wa-Closed Sets in Topological Spaces

Year 2014, Volume: 3 Issue: 7, 7 - 19, 01.07.2014

S. S. Benchalli

Abstract

The aim of this paper is to introduce a new class ofclosed sets called gωα-closed sets using ωα-closed sets in topological spaces. This class is independent of ωα-closed sets. This newclass of set lies between the class of α-closed sets and the class ofαg-closed sets. Some of their properties are investigated. We alsodefine and study the gωα-closure and gωα-interior in topologicalspaces

Keywords

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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 J. Pure Appl. Math. 21, (1990), 717?719.
• P. Bhattacharyya and B.K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math., 29, (1987), 376?382.
• S. S. Benchalli, P. G. Patil and T. D. Rayanagaudar, ωα-Closed sets is Topological Spaces, The Global. J. Appl. Math. and Math. Sci,. 2, 2009, 53-63.
• J.Dontchev, On Generalizing Semi-Pre-Open sets, Mem. Fac. Kochi Univ (Math, 16, 1995, 35-48.
• Y.Gnanambal, On Generalized Pre-Regular Closed Sets in Topological Spaces, In- dian. J. pure appl. Math, 28(3), 1997 351-360.
• 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, Rent. Circ. Mat. Palermo, 19(2), 1970 89-96.
• H. Maki, R. Devi, and K. Balachandran, Generalized α-Closed Sets in Topol- ogy,Bull. Fukuoka Univ, Ed., Part III., 42, 1993, 13-21.
• H. Maki, R. Devi, and K. Balachandran, Associate 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. Mashhour, M. E. Abd El-Monsef, and S. N. EL-Deeb, α-Open Mappings, Acta. Math. Hungar., 41, 1983 213-218.
• N. Nagaveni, Studies on Generalizations of Homeomorphisms in Topological Spaces, Ph.D. Thesis, Bharathiar University, Coimbatore., 1999.
• O. Njastad, On Some Classes of Nearly open Sets, Pacific. J. Math., 15, 1965 961-970.
• N. Palaniappan and K.C. Rao, Regular generalized closed sets, Kyungpook Math. J. 33, (1993), 211?219.
• A. Pushpalatha, Studies on Generalizations of Mappings in Topological Spaces, Ph.D.Thesis, Bharathiar University, Coinbatore.
• M. Stone, Application of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41, (1937), 374?481.
• P. Sundaram, and N. Navalagi, On Weakly Generalized Continuous Maps, Weakly Generalized Closed Maps and Weakly Generalized Irresolute Maps, Far East. J. Math Sci., 6, 1998.
• P. Sundaram, and M. Shrik John, On ω-Closed Sets in Topology, Acta Ciencia Indica, 4, 2000, 389-392.
• M. K. R. S. Veera Kumar, g∗-preclosed sets, Acts Ciencia indica, 28(1), 2002, 51-60. [23] M. K. R. S. Veera Kumar, On α-Generalized-Regular Closed Sets, Indian Journal of Mathematics., 44(2), 2002, 165-181.