Ss-Open sets and Ss-Continuous Functions

  • Authors

    • Alias B. Khalaf University of Duhok
    • Abdulrahman H. Majeed
    • Jamil M. Jamil
    2014-02-14
    https://doi.org/10.14419/ijams.v2i1.1761
  • Abstract

    In this paper we introduce and study the concept of Ss-open sets .also, a study new class of functions called Ss-continuous functions, the relationships between Ss-continuity and other types of continuity are investigated.

    Keywords: Ss-open set, Ss-continuous function, semi-open set, semi-continuous functions.

  • References

    1. M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, B-open sets and B-continuous mappings, Bull. Fac. Sci.Assuit. Univ., 12 (1) (1983), 1-18.
    2. N. K. Ahmed, On Some Types of Separation Axioms, M. Sc. Thesis, College of Science, Salahaddin Univ., (1990).
    3. M. Caldas, S. Jafari, T. Noiri and R. Saraf, Functions with strongly semi-µ-closed graphs, J. of Advanced Research in Applied Mathematics 2(2) (2010), 38-47.
    4. D. E. Cameron, Properties of S-closed spaces, Proc. Amer. Math. Soc. 72 (1978), 581-586.
    5. S. G. Crossley and S. K. Hildebrand, Semi-closure, Texas J. Sci., 22 (1971), 99-112.
    6. G. Di Maio and T. Noiri, On s-closed spaces, Indian J. Pure Appl. Math., 18 (3) (1987), 226-233.
    7. J. Dontchev, on submaximal spaces, Tamkang Math. J., 26(1995), 243-250.
    8. J. Dontchev and M. Ganster , On covering space with semi regular sets, Ricerche di Matematica, 45(1), (1996), 229-245.
    9. J. Dontchev, Contra-continuous functions and strongly S-closed spaces, Internat. J. Math. and Math. Sci., 19 (2) (1996), 303-310.
    10. J. Dontchev and T. Noiri, Contra-Semi-Continuous Functions, Mathematica Pannonica, 10(2)(1999), 159-168.
    11. C. Dorsett, Semi-regular spaces, Soochow J. Math, 8(1982), 45-53.
    12. K. Dlaska, N. Ergun and M. Ganster, On the topology generated by semi-regular sets, Indian J. Pure Appl. Math., 25(11) (1994), 1163-1170.
    13. J. E. Joseph and M. H. Kwack, On S-closed spaces, Proc. Amer. Math. Soc., 80 (2) (1980), 341-348.
    14. A. B. Khalaf and Z. H. Ameen, Sc-open sets and Sc-continuous functions, J. of Advanced Research in Pure Mathematics, 2 (3) (2010), 87-101.
    15. A. B. Khalaf and N. K. Ahmed, SB -open sets and SB-continuous functions, Thai J. Math., 11(2) (2013), 319-335.
    16. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1) (1963), 36-41.
    17. A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and week precontinuous mappings, Proc. Math. Phys. Soc., [Egypt], 53 (1982), 47-53.
    18. O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15 (3) (1965), 961-970.
    19. N. Puturong, On strongly µ-semi-continuous functions, Thai Journal of Mathematics, Special Issue Annual Meeting in Mathematics, (2007), 11-23.
    20. H. A. Shareef, Sp-Open Sets, Sp-Continuity and Sp-Compactness in Topological Spaces , M. Sc. Thesis, University of Sulaimani (2007).
    21. J. N. Sharma, Topology ( General and Algebraic), Krishna Parkashan Mandir, 4th Edition (2011).
    22. S. F. Tadros and A. B. Khalaf, On regular semi-open sets and s*-closed spaces, Tamkang J. of Math., 23 (4) (1992), 337-348.
    23. N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl., 78 (2) (1968), 103-118.
    24. R. H. Yunis, Properties of µ-semi-open sets, Zanco J. of Pure and Applied Sciences, 19 (1) (2007), 116-122.
  • Downloads

  • How to Cite

    Khalaf, A. B., H. Majeed, A., & M. Jamil, J. (2014). Ss-Open sets and Ss-Continuous Functions. International Journal of Advanced Mathematical Sciences, 2(1), 71-80. https://doi.org/10.14419/ijams.v2i1.1761