Slightly πgγ-Continuous Functions

Year 2013, Volume: 2 Issue: 3, 60 - 71, 01.03.2013

O. Ravi S.margaret Parimalam

Abstract

–generalized γ-continuous functions is introduced. Basic properties of slightly π-generalized γ-continuous functions are studied.The class of slightly π-generalized γ-continuous functions properly includes the class of slightly gγ-continuous functions andπgγ-continuous functions. Also, by using slightly π-generalizedγ-continuous functions, some properties of domain/range of functions are characterized

Keywords

–continuity, slight πgγ-continuity, πgγ-continuity, πgγ-closed set, πGγO-connectedness

References

• M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, β-open sets and β- continuous mappings, Bull. Fac. Sci. Assiut Univ., 12(1983), 77-90.
• M. Akdag and A. Ozkan, Some properties of contra gb-continuous functions, Jour- nal of New Results in Science, 1(2012), 40-49.
• S. C. Akgun and G. Ashm, On πgb-closed sets and related topics, International Journal of Mathematical Archive, 3(5)(2012), 1873-1884.
• A. K. Al-Obiadi, π-generalized b-closed sets in topological spaces, IBN AL- HAITHAM J. FOR PURE & APPL. SCi., 24(3)(2011),
• A. Al-Omari and M. S. M. Noorani, Generalized b-closed sets, Bull. Malays. Math. Sci. Soc., (2)32(1)(2009), 19-30.
• D. Andrijevic, On b-open sets, Mat. Vesnik, 48(1-2)(1996), 59-64.
• S. C. Arora and S. Tahiliani, Slightly generalized β-continuous functions, Sarajevo J. Math., 9(21)(2013), 143-152.
• C. W. Baker, Slightly precontinuous functions, Acta Math. Hungar., 94(1-2)(2002), 45
• J. Cao, M. Ganster and I. Reilly, On sg-closed sets and gα-closed sets, Mem. Fac. Sci. Kochi Univ. Math., 20(1999), 1-5.
• C. Carpintero, N. Rajesh and E. Rosas, On slightly πg-continuous functions, Jour- nal of Advanced Research in Pure Mathematics, 3(3)(2011), 115-127.
• J. Dontchev and M. Przemski, On the various decompositions of continuous and some weakly continuous functions, Acta Math. Hungar., 71(1-2)(1996), 109-120.
• J. Dontchev and T. Noiri, Quasi-normal spaces and πg-closed sets, Acta Math. Hungar., 89(3)(2000), 211-219.
• E. Ekici, On γ-normal spaces, Bull. Math. Soc. Sci. Math. Roumanie (N. S), 50(98)(2007), 259-272.
• E. Ekici and C. W. Baker, πg-closed sets and continuity, Kochi J. Maths., 2(2007), 35
• E. Ekici and M. Caldas, Slighly γ-continuous functions, Bol. Soc. Parana. Math., (3)22(2)(2004), 63-74.
• A. A. El-Atik, A study on some types of mappings on topological spaces, Master’s Thesis, Tanta University, Egypt, 1997.
• M. Fujimoto, S. Takigawa, J. Dontchev, T. Noiri and H. Maki, The topological structure and groups of digital n-spaces, Kochi J. Math., 1(2006), 31-55.
• M. Ganster and D. Andrijevic, On some questions concerning semi-preopen sets, J. Inst. Math. Compu. Sci. Math., 1(1988), 65-75.
• A. Keskin and T. Noiri, On bD-sets and associated separation axioms, Bulletin of the Iranian Mathematical Society, 35(1)(2009), 179-198.
• R. M. Latif, Characterizations and applications of γ-open sets, Soochow J. Math., 32(3)(2006), 1-10.
• N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(2)(1970), 89-96.
• H. Maki, Generalized ∧-sets and the associated closure operator, The special issue in commemoration of Prof. Kazusda IKEDA’s Retirement (1986), 139-146.
• O. Ravi, G. Selvi, S. Murugesan and A. Pandi, Slightly gγ-continuous functions, submitted. A. R. Singal and R. C. Jain, Slightly continuous mappings, J. Indian Math. Soc., 64(1997), 195-203.
• D. Sreeja and C. Janaki, On πgb-closed sets in topological spaces, International Journal of Mathematical Archive, 2(8)(2011), 1314-1320.
• R. Staum, The algebra of a bounded continuous functions into a nonarchimedian field, Pacific J. Math., 50(1974), 169-185.
• L. A. Steen and J. A. Seebach Jr, Counterexamples in topology, Holt, Rinenhart and Winston, New York, 1970.
• M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Am. Math. Soc., 41(1937), 375-381.
• V. Zaitsev, On certain classes of topological spaces and their bicompactifications, Dokl. Akad. Nauk. SSSR 178(1986), 778-779.
• I. Zorlutuna, M. Kucuk and Y. Kucuk, Slightly generalized continuous functions, Kochi J. Math., 3(2008), 99-108.