Anew Types of Contra Continuity in Bi-Supra Topological Space
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Abstract
In this paper we introduce a new class of functions in bi-supra topological space called (contra-i[contra-ii]-continuous, contra-g-i[contra-g-ii]-continuous,contra-gα-i[contra-gα-ii]-continuous, contra-gr-i[contra-gr-ii]-continuous, contra-gb-i[contra-gb-ii]-continuous, contra-πg-i[contra-πg-ii]-continuous, contra-πgα-i[contra-πgα-ii]-continuous, contra-πgr-i[contra-πgr-ii]-continuouos, contra-πgb-i[contra-πgb-ii]-continuous) and we study the relation among these functions and the composition of these functions. At last many important theorems are proved.
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References
[1] Ahmad Al-Omari and Mohd. Salmi Md. Noorani, On Generalized b-closed sets. Bull. Malays. Math. Sci. Soc(2),19-30, 32(1) (2009).
[2] A.S. Mashour, M.E. Abd El- Monsef and S.N. El-Deep. On Precontinuous and weak pre continuous mappings, Proc, Math, Phys. Soc. Egypt., 53, 47-53. 1982.
[3] C.Janaki, Studies on πgα-closed sets in Topology, Ph. D Thesis, Bharathiar University, Coimbatore (2009).
[4] C.Janaki and V.Jeyanthi-A New Class of Contra Continuous Functions in Topological Spaces-International Refereed Journal of Engineering and Science (IRJES),44-51, 2(2013).
[5] D. Andrijevic, On b-open sets, Mat. Vesnik 48, 59-64,(1996).
[6] D.Andrijevic. Semi- preopen sets, Mat. Vesnik, 38 (1), 24-32. (1986).
[7] E.Ekici, On Contra πg-continuous functions, Chaos, Solitons and Fractals, 71-81,35 (2008).
[8] H. Maki, P.Sundaram and K. Balachandran: On Generalized homeomorphisms in topological spaces. Bulletin of Fukuoka Uni. Of Edn. Vol.40, Part III,13-21,(1991).
[9] H. Maki, R. Devi and K. Balachandran, Associated topologies of generalized α –closed sets and-generalized closed sets, Mem. Sci. Kochi Univ. Ser. A. Math.51–63,15(1994).
[10] I.Arokiarani, K. Balachandran and C.Janaki, On contra-πgα-continuous functions, Kochi. J. Math., (3),201-209, (2008).
[11] J. Dontchev and T. Noiri, Quasi-normal spaces and πg-closed sets, Acta Math. Hungar. 89, 211–219, (3) (2000).
[12] J. Dontchev, Contra – continuous function and strongly S-closed spaces, Internat. J.Math. Math. Sci. 19,303-310, (1996).
[13] Jeyanthi.V, 2Janaki.C, πgr-Closed Sets In Topological Spaces, Asian Journal of Current Engineering and Maths,241 – 246. 1: 5 Sep –Oct (2012).
[14] Kelley, J.C. “Bi-topological space ”,proc London , math Soc., 71-89 (1963).
[15] Mashhour, S., M.E. Abd El-Monsef and S.N. El-Deep, onphys. Soc. Egypt, 53: 47-53, (1983).
[16] M. Caldas, S. Jafari, T. Noiri and M. Simoes, A new generalization of contra-continuity via Levineʼs g-closed sets, Chaos, Solitons and Fractals 32, 1597-1603, (2007).
[17] Metin Akdag and Alkan Ozkan- Some Properties of Contra gb-continuous Functions-Journal of New Results in Science ,40-49,1 (2012).
[18] M.H. Stone. Application of the Theory Boolean rings to general topology, Trans.Amer.Math.Soc.,41, 375-381. (1937).
[19] N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo 19, 89– 96, (1970).
[20] N. Levine. Semi-open sets, semi-continuity in topological spaces, Amer Math, Monthly, 70, 36-41. (1963).
[21] O. Njastad. On some classes of nearly open sets, Pacific J. Math. 15, 961-970. (1965).
[22] S. Bhattacharya, On generalized regular closed sets, Int. J. Contemp. Math. Sciences, Vol. 6, no. 145-152, (201).
[23] S.I. Mahmood, On Generalized Regular Continuous Functions in Topological spaces, Ibn Al- Haitham Journal for pure and applied sience, No.3, Vol .25,377-385 ,(2012).
[24] Sreeja .D and Janaki. C, On Contra πgb-continuous functions in topological spaces, International Journal of Statistika and Mathematika, E-ISSN-2239-8605, Vol 1 , issue 2,pp 46-51, (2011).
[25] V. Zaitov. On certain classes of topological spaces and their bicompactification, Dokl Akad Nauk SSSR. 178: 778-9. (1968).