\({\lambda}_{pc}\)-Open Sets and \({\lambda }_{pc}\)-Separation Axioms

  • Authors

    • Alias B. Khalaf University of Duhok
    • Alan Omar University of Duhok
    2014-05-26
    https://doi.org/10.14419/ijbas.v3i2.2521

  • The aim of this paper is to introduce a new class of sets called \({\lambda }_{pc}\text{-}\) open sets and to investigate some of their relationships and properties. Further, by using this set, the notion of \({\lambda}_{pc}\text{-}{T}_\text{i}\) spaces \(( i = 0,1/2, 1, 2 )\) and \({\lambda}_{pc}\text{-}{R}_{j}\) spaces \(( j = 0, 1 )\) are introduced and some of their properties are investigated.

    Keywords: s-operation; \({\lambda }_{pc}\)-Open Set; \({\lambda }_{pc}-T_i, i=0,1,2\); \({\lambda }_{pc}-R_j, j=0,1.\)

    Author Biography

    • Alias B. Khalaf, University of Duhok
      Professor, Department of Mathematics

  • References

    1. B. Ahmad and S. Hussain, Properties of -operations in topological spaces, Aligarh Bull. Math., 22(1):45-51,2003.
    2. H. Maki, J. Umehara, and T. Nori, Every Topological Space is Pre{T1=2, Mem. Fac. Sci. Kochi Univ. Ser.A(Mathes.), 17(1996), 33-42.
    3. S. G. Crossley and S. K. Hildebrand, Semi-closure, Texas J. Sci., 22:99-112, 1971.
    4. H. Corson and E. Michael, Metrizability of certain countable union, Illinois J. Math., 8(1964), 351-360.
    5. M. Caldas, S. Jafari, and T. Nori, Characterizations of pre-R0, and pre-R1 topological spaces, Topology Pro-ceedings, 25(2000), 17-30.
    6. S. Kasahara, Operation-compact spaces, Math. Japonica, 24:97-105, 1979.
    7. A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On pre-continuous and week precontinuous mappings,Proc. Math. Phys. Soc., [Egypt], 53(1982), 47-53.
    8. N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19:89-96, 1970.
    9. A. Chattopadhyay, pre-T0 and pre-T1 Topological Spaces, J. Indian Acad. Math., 17(2),(1995), 156-159.
    10. H. Ogata, Operation on topological spaces and associated topology, Math. Japonica, 36(1):175 -184, 1991.

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  • How to Cite

    Khalaf, A. B., & Omar, A. (2014). \({\lambda}_{pc}\)-Open Sets and \({\lambda }_{pc}\)-Separation Axioms. International Journal of Basic and Applied Sciences, 3(2), 137-145. https://doi.org/10.14419/ijbas.v3i2.2521