A Survey of Some Aspects on the Research Work of Fuzzy Topology in China

  • Pu Bao-ming
  • Liu Ying-ming


The fundamental concept of a fuzzy set, introduced by Zadeh in 1965 [34] provides a natural foundation for treating mathematically the fuzzy phenomena which exist pervasively in our real world and for building new branches of fuzzy mathematics. In the area of fuzzy topology much research has been carried out since 1968 [1].


Topological Space Neighborhood Structure Neighborhood System Fuzzy Point Separation Axiom 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 191–201.MathSciNetCrossRefGoogle Scholar
  2. 2.
    M. A. Erceg, Metric spaces in fuzzy set theory, J. Math. Anal. Appl., 69 ( 1979, 205–230.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    T. E. Gantner and R. C. Steinlage and R. H. Warren, Compactness in fuzzy topological spaces, J. Math. Anal. Appl., 62 (1978), 547–562.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Hu Cheng-Ming, A class of fuzzy topological spaces I, II, Neimenggu Daxue Xuebao 1 (1981), (in Chinese).Google Scholar
  5. 5.
    Hu Cheng-Ming, A metrization of fuzzy topological spaces, Ziran Zazhi 7 (1981), 554, (in Chinese).Google Scholar
  6. 6.
    B. Hutton, Uniformities on fuzzy topological spaces, J. Math. Anal. Appl., 58 (1977), 559–571.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Jiang Ji-Quang, Separation axioms in fuzzy topological spaces and fuzzy compactness, Sichuan Daxue Xuebao 3 (1979), 1–10, (in Chinese).Google Scholar
  8. 8.
    Jiang Ji-Quang, Concerning separation axioms for induced fuzzy topological spaces, Trans. Sichuan Math. Soc., 1 (1981), 25–31, (in Chinese).Google Scholar
  9. 9.
    Jiang Ji-Quang, On fuzzy countably compact spaces and fuzzy sequentially compact spaces, Sichuan Daxue Xuebao, 1 (1980), 37–43, (in Chinese).Google Scholar
  10. 10.
    Jiang Ji-Quang, Fuzzy paracompact spaces, ibid, 3 (1981), 4752, (in Chinese).Google Scholar
  11. 11.
    Jiang Ji-Quang, Weight, charactor, and density of L-fuzzy topological spaces, Acta Mathematica Scientia, (to appear) (in Chinese).Google Scholar
  12. 12.
    J. L. Kelley, General Topology, Van Nostrand, 1955.Google Scholar
  13. 13.
    R. Lowen, A comparison of different compactness notions in fuzzy topological spaces, ibid., 64 (1978), 446–454.MathSciNetMATHGoogle Scholar
  14. 14.
    Li Zhongfu, On the generalization of C. T. Yang’s theorem concerning derived set in fuzzy topology, Fuzzy Math., 1 (1981), 39–42, (in Chinese).MathSciNetGoogle Scholar
  15. 15.
    Li Zhongfu, A class of L-fuzzy topological spaces I. Neighborhood structures of L-fuzzy points, J. Math. Research and Exposition, 2 (1982), 1: 37–44, (in Chinese).Google Scholar
  16. 16.
    Liu Ying-Ming, A note on compactness in fuzzy unit interval, Kexux Tongbao 25 (1980), A special issue of Math., Phy., and Chem., 33–35, (in Chinese).Google Scholar
  17. 17.
    Liu Ying-Ming, Compactness and Tychonoff theorem in fuzzy topological spaces, Acta Mathematica Sinica, 24 (1981), 260–268, (in Chinese).MathSciNetGoogle Scholar
  18. 18.
    Liu Ying-Ming, Intersection operation on union-preserving mappings in completely distributive lattices, J. Math. Anal. Appl., 84 (1981), 249–255.MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Liu Ying-Ming, Inverse operation on union-preserving mappings in lattices and its applications to fuzzy uniform spaces, Proc. of 12th International Symposium on Multiple-Valued Logic, 280–288.Google Scholar
  20. 20.
    Liu Ying-Ming, A pointwise characterization of fuzzy completely regularity and imbedding theorem in fuzzy topological spaces, Scientia Sinica, 1982, 8: 673–680.Google Scholar
  21. 21.
    Liu Ying-Ming, On the fuzzy Stone-Céch compactification, Acta Math. Sinica, (to appear) (in Chinese), for English abstract see Kexue Tongbao, 27 (1982), 7: 799.Google Scholar
  22. 22.
    Liu Ying-Ming, Neighborhood structures in fuzzy topological spaces, Kexue Tongbao, 27 (1982), 3:189–190, (abstract in Chinese).Google Scholar
  23. 23.
    Liu Ying-Ming, Some properties of fuzzy convex sets, to appear in JMAA. (A detailed abstract in Chinese has been published in Kexue Tongbao, 27 (1982), 6: 328–330 ).Google Scholar
  24. 24.
    H. W. Martin, A Stone-tech ultra fuzzy compactification, J. Math. Anal. Appl., 73 (1980), 453–456.MathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    Pu Pao-Ming and Liu Ying-Ming, Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Annal. Appl., 76 (1980), 571–599. (Also see Sichuan Daxue Xuebao 1 (1977), 31–50, (in Chinese).)Google Scholar
  26. 26.
    Pu Pao-Ming and Liu Ying-Ming, Fuzzy topology II, Product and quotient spaces, J. Math. Anal. Appl., 77 (1980), 20–37. (A detailed abstract in Chinese has also been published in Kexue Tongbao, 24 (1979), No. 3, 97–100.)Google Scholar
  27. 27.
    Pu Si-Li, Mapping properties of induced fuzzy topological spaces, (in Chinese).Google Scholar
  28. 28.
    Pu Si-Li, Zero-dimensional fuzzy topological spaces, (in Chinese).Google Scholar
  29. 29.
    Pu Si-Li, A better definition on fuzzy boundary, Fuzzy Math., 2 (1982), 21–34, (in Chinese).MathSciNetGoogle Scholar
  30. 30.
    Wang Guo-Jun, Topological molecular lattices (I), Sanshi Sida Xuebao, 1 (1979), 1–15, (in Chinese).Google Scholar
  31. 31.
    Wang Guo-Jun, Separation axioms in topological molecular lattices, J. Math. Research and Exposition, (to appear).Google Scholar
  32. 32.
    Wang Guo-Jun, A new fuzzy compactness defined by fuzzy nets, J. Math. Anal. Appl., (to appear).Google Scholar
  33. 33.
    M. D. Weiss, Fixed points, separation and induced topologies for fuzzy sets, J. Math. Anal. Appl., 50 (1975), 142–150.MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353.MathSciNetMATHCrossRefGoogle Scholar
  35. 35.
    Zhou Hao-Xuan, Relations between topological spaces and fuzzy topological spaces, (in manuscript).Google Scholar
  36. 36.
    Peng Yuwei, Fuzzy function spaces, (to appear), (in Chinese).Google Scholar
  37. 37.
    Liang Jihua, Some problems on fuzzy metric spaces, (to appear), (in Chinese).Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • Pu Bao-ming
    • 1
  • Liu Ying-ming
    • 1
  1. 1.Institute of MathematicsSichuan UniversityChengdu, SichuanChina

Personalised recommendations