Almost α-γ-Irresolute Functions

Year 2014, Volume: 3 Issue: 7, 20 - 28, 01.07.2014

O. Ravi

Abstract

functions called almost γ-irresolute functions and almost α-γirresolute functions in topological spaces. We obtain several characterizations of these classes and study their properties and investigate the relationships with the known non-continuous functions

Keywords

semi-open set, preopen set, βopen set, γ-open set, almost αγ-irresolute function

References

• Abd El-Monsef, M.E., El-Deeb, S.N. and Mahmoud, R.A. (1983) : β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ. 12, 77-90.
• Abd El-Monsef, M.E., Geaisa, A.N. and Mahmoud, R.A. (1985) : β-regular spaces, Proc. Math. Phys. Soc., Egypt, 60, 47-52.
• Andrijevi´c, D. (1986) : Semi-preopen sets, Mat. Vesnik, 38, 1, 24-32: MR 87; 54002.
• Andrijevi´c, D. (1996) : On b-open sets, Mat. Vesnik, 48, 59-64.
• Beceren, Y. (2000a) : On strongly α-continuous functions, Far East J. Math. Sci., Special Vol., I, 51-58.
• Beceren, Y. (2000b) : On semi α-irresolute functions, J. Indian Acad. Math., 22, 353-362: MR 1830892.
• Beceren, Y. (2000c) : Almost α-irresolute functions, Bull. Cal. Math. Soc., 92, 3, 213-218.
• Cammaroto, F. and Noiri, T. (1989) : Almost irresolute functions, Indian J. Pure Appl. Math., 20, 5, 472-482.
• Chae, G.I., Noiri, T. and Lee, D.W. (1986) : On na-continuous functions, Kyung- pook Math. J., 26, 1, 73-79.
• Crossley, S.G. and Hildebrand, S.K. (1972): Semi-topological properties, Fund. Math., 74, 3, 233-254.
• Dube, K.K., Lee, J.Y. and Panwar, O.S. (1983) : A note on semi-closed graphs, Ulsan Inst. Tech. Rep., 14, 2, 379-383.
• El-Atik, A.A. (1997): A study on some types of mappings on topological spaces, Master’s Thesis, Tanta University, Egypt.
• El Naschie, MS., Rossler, OE. and Oed, G. (1996) : Information and diffusion in quantum physics, Chaos, Solitons & Fractals, 7, 5, (special issue).
• El Naschie, MS. (2004) : Quantum gravity, Clifford algebra, fuzzy set theory and the fundamental constants of nature, Chaos, Solitons & Fractals, 20, 437-450.
• El Naschie, MS. (2004) : The symplistic vacuum, exotic quasi-particles and gravi- tational instanton, Chaos, Solitons & Fractals, 22, 1-11.
• Ganster, M. and Steiner, M. (2007): On some questions about b-open sets, Ques- tions and Answers in general topology, Online.
• Jankovi´c, D.S. (1983) : On locally irreducible spaces, Ann. Soc. Sci. Bruxelles, S´er, I 97, 2, 59-72.
• Keskin, A. and Noiri, T. (2009): Almost b-continuous functions, Chaos, Solitons and Fractals, 41, 72-81.
• Levine, N. (1963) : Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70, 1, 36-41.
• Maheshwari, S.N. and Thakur, S.S. (1980) : On α-irresolute mappings, Tamkang J. Math., 11, 2, 209-214.
• Mahmoud, R.A. and Abd El-Monsef, M.E. (1990) : β-irresolute and β-topological invariant, J. Pakistan Acad. Sci., 27, 285-296.
• Mashour, A.S., Abd El-Monsef, M.E. and El-Deeb, S.N. (1982) : On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53, 47-53.
• Mashhour, A.S., Hasanein, I.A. and El-Deeb, S.N. (1983) : α-continuous and α- open mappings. Acta Math. Hungar., 41, 3-4, 213-218: DOI: 10. 1007/BF01961309. [24] Nasef, A.A and Noiri, T. (1997) : Some weak forms of almost continuity, Acta Math. Hungar., 74, 3, 211-219. DOI: 10. 1023/A: 1006507816942.
• Nasef, A.A and Noiri, T. (1998) : Strong forms of faint continuity, Mem. Fac. Sci. Kochi Univ. Ser. A Math., 19, 21-28.
• Nj ˙astad, O. (1965) : On some classes of neariy open sets, Pacific J. Math., 15, 3, 961-970: DOI: 10. 2140/pjm.1965.15.961.
• Noiri, T. and Popa, V. (1990): Weak forms of faint continuity, Bull. Math. Soc. Sci. Math. R.S. Roumanie (N.S.), 34 (82), 263-270.
• Noiri, T. and Popa, V. (2010): On decompositions of continuity in topological spaces, Acta Math. Hungar., 128, 1-2, 175-189. DOI: 10.1007/s10474-010-9179-6. [29] Rajesh, N. (2007): On θ-b-irresolute functions, Sarajevo Journal of Mathematics, 3, 15, 115-122.
• Svozil, K. (1987): Quantum field theory on fractal space-time: a new regularization method. J Phys A Math Gen, 20, 3861-3875.