On Almost Continuity

  • Ekici, Erdal (Department of Mathematics, Canakkale Onsekiz Mart University)
  • 투고 : 2004.10.04
  • 발행 : 2006.03.23

초록

A new class of functions is introduced in this paper. This class is called almost ${\delta}$-precontinuity. This type of functions is seen to be strictly weaker than almost precontinuity. By using ${\delta}$-preopen sets, many characterizations and properties of the said type of functions are investigated.

키워드

참고문헌

  1. M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, ${\beta}$-open sets and ${\beta}$-continuous mappings, Bull Fac. Sci. Assiut Univ., 12(1983), 77-90.
  2. D. Andrijevic, Semi-preopen sets, Mat. Vesnik, 38(1986), 24-32.
  3. N. Bourbaki, General Topology, Part I, addison Wesley, reading, Mass., (1996).
  4. D. Carnahan, Some Properties Related to Compactness in Topological Spaces, Ph. D. Thesis (Univ. Arkansas, 1973).
  5. S. G. Crossley and S. K. Hildebrand, Semi-closure, Texas J. Sci., 22(1971) 99-112.
  6. E. Ekici, (${\delta}$-pre,s)-continuous functions, Bulletin of the Malaysian Mathematical Society, accepted (2004).
  7. A. A. El-Atik, A study of some types of mappings on topological spaces, MSc Thesis, Tanta Univ., Egypt, (1997).
  8. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41. https://doi.org/10.2307/2312781
  9. P. E. Long and L. L. Herrington, The $T_{\theta}$-topology and faintly continuous functions, Kyungpook Math. J., 22(1982), 7-14.
  10. A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47-53.
  11. A. A. Nasef and T. Noiri, Some weak forms of almost continuity, Acta Math. Hungarica, 74(3)(1997), 211-219. https://doi.org/10.1023/A:1006507816942
  12. A. A. Nasef, Another weak forms of faint continuity, Chaos, Solitons and Fractals, 12(2001), 2219-2225. https://doi.org/10.1016/S0960-0779(00)00156-9
  13. O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 96J-970.
  14. T. Noiri, On ${\delta}$-continuous functions, J. Korean Math. Soc., 16(1980), 161-166.
  15. T. Noiri, Characterizations of extremally disconnected spaces, Indian J. Pure Appl. Math., 19(1988), 325-329.
  16. T. Noiri, Almost ${\alpha}$-continuous functions, Kyungpook Math. J., 28(1988), 71-77.
  17. T. Noiri, On almost continuous functions, Indian J. Pure Appl. Math., 20(1989), 571-576.
  18. T. Noiri, Almost quasi-continuous functions, Bull. Inst. Math. Acad. Sinica, 18(1990), 321-332.
  19. T. Noiri and V. Popa, Weak forms of faint continuity, Bull. Math. Soc. Sci. Math. Roumanie, 34(82)(1990), 270-363.
  20. S. Raychaudhuri and M. N. Mukherjee, On ${\delta}$-almost continuity and ${\delta}$-preopen sets, Bull. Inst. Math. Acad. Sinica, 21(4)(1993), 357-366.
  21. M. K. Singal and A. R. Singal, Almost continuous mappings, Yokohama Math. J., 16(1968), 63-73.
  22. M. K. Signal and S. P. Arya, On almost-regular spaces, Glasnik Mat. III, 4(24)(1969), 89-99.
  23. M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937) 375-381. https://doi.org/10.1090/S0002-9947-1937-1501905-7
  24. N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. (2), 78(1968), 103-118.