ON WEAKLY e-CONTINUOUS FUNCTIONS

Year 2011, Volume: 40 Issue: 6, 781 - 791, 01.06.2011

Murad Özkoç  gülhan Aslım

Abstract

The main goal of this paper is to introduce and look into some of the fundamental properties of weakly e-continuous functions defined via eopen sets introduced by E. Ekici (On e-open sets, DP∗ -sets and DPE∗ - sets and decompositions of continuity, Arab. J. Sci. Eng. 33 (2A), 269–281, 2008). Some characterizations and several properties concerning weakly e-continuous functions are obtained. The concept of weak e-continuity is weaker than both the weak continuity introduced by N. Levine (A decomposition of continuity in topological spaces, Amer. Math. Monthly 68, 44–46, 1961) and the e-continuity introduced by Ekici, but stronger than weak β-continuity introduced by Popa and Noiri (Weakly β-continuous functions, An. Univ. Timis.Ser.Mat.-
Inform. 32 (2), 83–92, 1994). In order to investigate some different properties we introduce the concept of e-strongly closed graphs and also investigate relationships between weak e-continuity and separation axioms, and e-strongly closed graphs and covering properties.

Keywords

Faint e-continuity, e-T2 space, e-strongly closed graph, e-Lindel¨of space, Weak e-continuity, 2000 AMS Classification: 54 C 05

ON WEAKLY e-CONTINUOUS FUNCTIONS

Abstract

References

• Abd El-Monsef, M. E., El-Deeb, S. N. and Mahmoud, R. A. β-open sets and β-continuous mappings, Bull-Fac. Sci. Assiut Univ. 12, 77–90, 1983.
• Andrijevi`c, D. On b-open sets, Mat. Vesnik 48, 59–64, 1996.
• Andrijevi`c, D. Semi-preopen sets, Mat. Vesnik 38, 24–32, 1986.
• Bourbaki, N. General Topology (Part I) (Addison Wesley, Reading, MA, 1966).
• Dontchev, J. and Przemski, M. On the various decompositions of continuous and some weakly continuous functions, Acta Math. Hungar. 71 (1–2), 109–120, 1996.
• Ekici, E. New forms of contra continuity, Carpathian J. Math. 24 (1), 37–45, 2008.
• Ekici, E. On e-open sets, DP*-sets and DPE*-sets and decompositions of continuity, Arab. J. Sci. Eng. 33 (2A), 269–281, 2008.
• El-Atik, A. A. A Study on some Types of Mappings on Topological Spaces (MSc Thesis, Tanta University, Egypt, 1997).
• Levine, N. A decomposition of continuity in topological spaces, Amer. Math. Monthly 68, –46, 1961.
• Levine, N. Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly , 36–41, 1963.
• Long, P. E. and Herrington, L. L. The Tθ-topology and faintly continuous functions, Kyung- pook Math. J. 22, 7–14, 1982.
• Mashhour, A. S., Abd El-Monsef, M. E. and El-Deeb, S. N. On precontinuous and weak precontinuous functions, Proc. Math. Phys. Soc. Egypt 53, 47–53, 1982.
• Nasef, A. A. Another weak form of faint continuity, Chaos Solitons Fractals 12 (12), 2219– , 2001.
• Nj˚astad, O. On some classes of nearly open sets, Pacific J. Math. 15, 961–970, 1965.
• Noiri, T. Between continuity and weak continuity, Boll. Unione Mat. Ital. 9 (4), 647–654, Noiri, T. Weakly α-continuous functions, Int. J. Math. Sci. 10, 483–490, 1987.
• ¨Ozko¸c, M. and Aslım, G. On strongly θ-e-continuous functions, Bull. Korean Math. Soc. Park, J. H. Strongly θ-b-continuous functions, Acta Math. Hungar. 110 (4), 347–359, 2006.
• Park, J. H., Lee, B. Y. and Son, M. J. On δ-semiopen sets in topological space, J. Indian Acad. Math. 19 (1), 59–67, 1997.
• Porter, J. and Thomas, J. On H-closed and minimal Hausdorff spaces, Trans. Amer. Math. Soc. 118, 159–170, 1974.
• Popa, V. and Noiri, T. Weakly β-continuous functions, An. Univ. Timis. Ser. Mat.-Inform. (2), 83–92, 1994.
• Raychaudhuri, S. and Mukherjee, M. N. On δ-almost continuity and δ-preopen sets, Bull. Inst. Math. Acad. Sin. 21 (4), 357–366, 1993.
• Stone, M. H. Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41, 375–381, 1937.
• Veliˇcko, N. V. H-closed topological spaces, Amer. Math. Soc. Transl. 78, 103–118, 1968.
• Viglino, G. C-compact spaces, Duke Math. J. 36, 761–764, 1969.
• Willard, S. and Dissanayake, U. N. B. The almost Lindel¨of degree, Canad. Math. Bull. 27 (4), –455, 1984.
• Willard, S. General Topology (Addison Wesley Publishing Company, London, 1970).
• Zippin, L. On semicompact spaces, Amer. J. Math. 57 (2), 27-341, 1935.