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International journal of fuzzy logic and intelligent systems : IJFIS v.9 no.2, 2009년, pp.115 - 127  
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L-pre-separation axioms in (2, L)-topologies based on complete residuated lattice-valued logic

Zeyada, Fathei M.    (Department of Mathematics, Faculty of Science, Al-Azhar University   ); Abd-Allahand, M. Azab    (Department of Mathematics, Faculty of Science, Al-Azhar University   ); Mousa, A.K.    (Department of Mathematics, Faculty of Science, Al-Azhar University  );
  • 초록

    In the present paper we introduce and study L-pre- $T_0$ -, L-pre- $T_1$ -, L-pre- $T_2$ (L-pre-Hausdorff)-, L-pre- $T_3$ (L-pre-regularity)-, L-pre- $T_4$ (L-pre-normality)-, L-pre-strong- $T_3$ -, L-pre-strong- $T_4$ -, L-pre- $R_0$ -, L-pre- $R_1$ -separation axioms in (2, L)-topologies where L is a complete residuated lattice.Sometimes we need more conditions on L such as the completely distributive law or that the " $\bigwedge$ " is distributive over arbitrary joins or the double negation law as we illustrate through this paper. As applications of our work the corresponding results(see[1,2]) are generalized and new consequences are obtained.


  • 주제어

    (2, L)-topology .   Complete residuated lattice .   Pre-open set .   Pre-separation axioms.  

  • 참고문헌 (21)

    1. U. Hohle, Characterization of L-topologies by L-valued neighborhoods, in:U. Hohle, S.E. Rodabaugh(Eds.),The Handbooks of Fuzzy Sets Series, vol. 3, Kluwer Academic Publishers, Dordrecht, pp. 389- 432, 1999 
    2. F.H. Khedr, F.M. Zeyada and O.R. Sayed,Onseparation axioms in fuzzifying topology, Fuzzy Sets and Systems, Vol. 119, pp.439?458, 2001 
    3. M.S. Ying, A new approach for fuzzy topology(II), Fuzzy Sets and Systems, vol. 47, pp. 221?232, 1992 
    4. Y. Yue and Fu-Gui Shi, On(L,M)-fuzzy quasi-uniform spaces, Fuzzy Sets and Systems, vol. 158, pp.1472?1485, 2007 
    5. Fathei M. Zeyada, A.M. Zahran and A.K. Mousa, L-continuity of functions between(2,L)-topological spaces based on complete residuated lattice-valuedlogic(submitted) 
    6. T. Kubiak, On Fuzzy Topologies, Ph.D. Thesis, Adam Mickiewicz University, Poznan, Poland,1985 
    7. K.I. Rosenthal, Quantales and their applications, Pit-man Research Notes in Mathematics, vol. 234, (Long-man, BurntMill, Harlow1990) 
    8. M.S. Ying, A new approach for fuzzy topology(I), Fuzzy Sets and Systems, vol. 39, pp.302?321, 1991 
    9. K.M. Abd El-Hakeim, F.M. Zeyada and O.R. Sayed, pre-Continuity and D(c,p)-continuity in fuzzifying topology, Fuzzy Sets and Systems, vol.119, pp. 459?471, 2001 
    10. K.M. Abd El-Hakeim, F.M.Zeyada and O.R.Sayed, Pre-separation axioms in fuzzifyingty, Fuzzy Systems and Mathematics, vol. 17, No. 1, pp.29?37, 2003 
    11. A.P. Sostak, On fuzzy topological structure, Suppl. Rend. Circ. Mat. Palermo(2), vol. 11, pp.89?103, 1985 
    12. A.M. Zahran, Fathei M. Zeyada, M. Azab Abd-Allah and M.M. Khalaf, Separation axioms in L-fuzzifying topology, Accepted for publication in The Far East Journal of Mathematical Sciences 
    13. G. Birkhoff, Lattice theory, 3rd ed., AMS Providence, RI, 1967 
    14. Fathei M. Zeyada, M. Azab Abd-Allah and M.M. Khalaf, A comment on and a characterization of the concept of complete residuated lattice, Journal of Non-linear Analysis and its Applications, vol. 1, pp. 29?31, 2008 
    15. J. Pavelka, On fuzzy logic II, Z. Math. Logic Gvund-lagen Math., vol. 25, pp.119?134, 1979 
    16. J.L. Kelley, Generaltopology, VanNostrand, NewYork, 1955 
    17. M.S. Ying, Fuzzifying topology based on complete residuated Lattice-valued logic(I), Fuzzy Sets and Sys-tems, vol. 56, pp. 337?373, 1993 
    18. J. Shen, Separation axiom in fuzzifying topology, Fuzzy Sets and Systems, vol. 57, pp.111?123, 1993 
    19. U. Hohle and A.P. Sostak, Axiomatic foundations of fixed-basis fuzzy topology,The Handbooks of Fuzzy Sets Series,Vol. 3, Kluwer Academic Publishers, Dor-drecht, pp.123?272, 1999 
    20. L.A. Zadeh, Fuzzy sets, Inform. Control, vol. 8, pp.338?353 
    21. U.Hohle, Upper semicontinuous fuzzy sets and appli-cations, J. Math. Anal. Appl. vol. 78, pp.659?673, 1980 

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