S??compactness in L-topological spaces


  • Fu-Gui Shi Beijing Institute of Technology.




L-topology, βa−cover, Sβ−compactness, β−cluster point.


In this paper, the notion of S??compactness is introduced in L-topological spaces by means of open ?a?cover. It is a generalization of Lowen’s strong compactness, but it is different from Wang’s strong compactness. Ultra-compactness implies S??compactness. S??compactness implies fuzzy compactness. But in general N-compactness and Wang’s strong compactness need not imply S??compactness.

Author Biography

Fu-Gui Shi, Beijing Institute of Technology.

Department of Mathematics, School of Science.


[1] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24(1968), 182—190.

[2] P. Dwinger, Characterizations of the complete homomorphic images of a completely distributive complete lattice, I, Nederl. Akad. Wetensch. indag. Math. 44(1982), 403—414.

[3] T.E. Gantner et al., Compactness in fuzzy topological spaces, J. Math. Anal. Appl. 62(1978), 547—562.

[4] G. Gierz, et al., A compendium of continuous lattices, Springer Verlag, Berlin, 1980.

[5] J.A. Goguen, The fuzzy Tychonoff theorem, J. Math. Anal. Appl. 43(1973), 734—742.

[6] T. Kubiák, The topological modification of the L-fuzzy unit interval, Chapter 11, in Applications of Category Theory to Fuzzy Subsets, S.E. Rodabaugh, E.P. Klement, U. H¨ohle, eds., 1992, Kluwer Academic Publishers, 275—305.

[7] Z.F. Li, Compactness in fuzzy topological spaces, Chinese Kexue Tongbao 6(1983), 321-323.

[8] Y.M. Liu, Compactness and Tychnoff Theorem in fuzzy topological spaces, Acta Mathematica Sinica 24(1981), 260-268.

[9] Y.M. Liu, M.K. Luo, Fuzzy topology, World Scientific, Singapore, 1997.

[10] R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl. 56(1976), 621-633.

[11] R. Lowen, A comparision of different compactness notions in fuzzy topological spaces, J. Math. Anal. Appl. 64(1978), 446—454.

[12] F.-G. Shi, A new form of fuzzy ?-compactness, submitted to Proyecciones, 2005.

[13] F.-G. Shi, Theory of L?-nested sets and L?-nest sets and its applications, Fuzzy Systems and Mathematics 4(1995), 65—72 (in Chinese).

[14] F.-G. Shi, A new notion of fuzzy compactness in L-topological spaces, Information Sciences, 173(2005) 35—48.

[15] F.-G. Shi, C.-Y. Zheng, O-convergence of fuzzy nets and its applications, Fuzzy Sets and Systems 140(2003), 499—507.

[16] G.-J. Wang, A new fuzzy compactness defined by fuzzy nets, J. Math. Anal. Appl. 94(1983), 1—23.

[17] G.-J. Wang, Theory of L-fuzzy topological space, Shaanxi Normal University Press, Xian, 1988. (in Chinese).

[18] D.-S. Zhao, The N-compactness in L-fuzzy topological spaces, J. Math. Anal. Appl. 128(1987), 64—70.



How to Cite

F.-G. Shi, “S??compactness in L-topological spaces”, Proyecciones (Antofagasta, On line), vol. 24, no. 2, pp. 153-165, Apr. 2017.