Connectedness in fuzzy closure space

  • Abstract
  • Keywords
  • References
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  • Abstract

    A fuzzy ?ech closure space (X, k) is a fuzzy set X with fuzzy ?ech closure operator k: IX ? IX where IX is a power set of fuzzy subsets of X, which satisfies k ( ) = , 1 ?2 ? k( 1 ) k( ?2 ), k ( 1 ?2 ) = k 1) ?k (?2) for all 1 , ?2 IX . A fuzzy topological space X is said to be fuzzy connected if it has no proper fuzzy clopen set.Many properties which hold in fuzzy topological space hold in fuzzy ?ech closure space as well. A ?ech closure space (X, u) is said to be connected if and only if any continuous map f from X to the discrete space {0, 1} is constant. In this paper we introduce connectedness in fuzzy ?ech closure space.

    Keywords: Connectedness in Fuzzy ?ech Closure Space, Connectedness in Fuzzy Topological Space, Fuzzy ?ech Closure Operator, Fuzzy ?ech Closure Space, Fuzzy Topological Space.

  • References

    1. L.A. Zadeh, Fuzzy sets, Inform. And Control 8 (1965) pp: 338-353.
    2. C.L. Chang, Fuzzy topological Space, J. Math. Anal. Appl., 24 (1968), pp: 182-190.
    3. P.M. Pu and Y. M. Liu, Fuzzy topology I. Neighbourhood structure of a fuzzy point and Moor- Smith convergence. J. Math. Anal. Appl., 76, (1980), pp: 571-599.
    4. R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl. 56(1976), pp: 621-633.
    5. A.S. Mashhour, M.H. Ghanim, Fuzzy closure space, J. Math. Anal. Appl., 106, (1985), pp: 154-170.
    6. C. Boonpok, On Continuous Maps in Closure Spaces, General Mathematics Vol. 17, (2009), No. 2.
    7. R. Gowri, G. Jegadeesan, Connectedness in fuzzy ?ech closure spaces, Asian Journal of current engineering and maths 2:5, (2013) pp: 326-328.
    8. K. S. Sethupathy Raja, S. Lakshmivarahan Connectedness in fuzzy topological space, Kybernetika- volume 13 (1977), number 3.
    9. U.D. Tapi, Bhagyashri A. Deole, note on connectedness in closure space, Impact J. Sci. Tech., Fiji Islands, Vol. 6, (2012), No. 1,pp: 43-46.
    10. K. K. Azad. On fuzzy semi continuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl. 82(1) (1981), 1432.




Article ID: 3394
DOI: 10.14419/ijamr.v3i4.3394

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