Document Type: Research Paper


1 Department of Mathematics, Ocean University of China, Qingdao, 266071, P. R. China

2 Department of Mathematics, Ocean University of China, Qingdao, 266071, P. R. China


In this paper, we establish the theory of fuzzy ideal convergence on
completely distributive lattices and give characterizations of some topological
notions. We also study fuzzy limit structures and discuss the relationship
between fuzzy co-topologies and fuzzy limit structures.


[1] J. Ad´amek, H. Herrlich and G. E. Strecker,Abstract and concrete categories, J. Wiley &

Sons, New York, 1990.

[2] C. L. Chang,Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182-193.


[3] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott,A compendium

of continuous lattice, Springer Verlag, Berlin/Heidelberg/New York.

[4] U. H¨ohle,Upper semicontinuous fuzzy sets and applications, J. Math. Anal. Appl., 78 (1980),



[5] U. H¨ohle and A. P. ˇSostak,Axiomatic foundations of fixed-basis fuzzy topology, Chapter 3 in:

H¨ohle U., Rodabaugh S. E.(Eds), Mathematics of Fuzzy Sets-Logic, Topology and Measure


Theory, Kluwer Academic Publishers (Boston/Dordrecht/London), (1999), 123-272.


[6] K. C. Min,Fuzzy limit spaces, Fuzzy Sets and Systems, 32 (1989), 343-357.

[7] T. Kubiak,On fuzzy topologies, (PhD Thesis, Adam Mickiewicz, Poznan, Poland, 1985.

[8] Y. M. Li,Limit structures over completely distributive lattices, Fuzzy Sets and Systems, 132

(2002), 125-134.

[9] S. E. Rodabaugh,Powerset operator foundations for poslat fuzzy set theories and topologies,

Chapter 2 in [5]: (1999), 91-116.


[10] S. E. Rodabaugh,Categorical foundations of variable-basis fuzzy topology, Chapter 4 in [5],



[11] A. P. ˇSostak,On a fuzzy topological structure, Rendiconti Ciecolo Matematico Palermo

(Suppl. Ser. II),11 (1985), 89-103.

[12] G. J. Wang,Theory of topological molecular lattices, Fuzzy Sets and Systems, 47 (1992),



[13] L. S. Xu,Characterizations of fuzzifying topologies by some limit structures, Fuzzy Sets and

Systems,123 (2001), 169-176.

[14] Z. Q. Yang,Ideals in topological molecular lattices, Acta Math.Sinica, 2 (1986), 276-279 (in



[15] M. Ying ,A new approach to fuzzy topology (I), Fuzzy Sets and Systems, 39 (1991), 303-321.

[16] Y. Yue and J. Fang,Categories isomorphic to the Kubiak-ˇSostak extension of TML, Fuzzy

Sets and Systems,157 (2006), 832-842.