Sequential S∗-compactness in L-topological spaces

  • Shu-Ping Li Mudanjiang Teachers College.
Palabras clave: L-topology, Constant a-sequence, Weak O-cluster point, Weak O-limit point, Sequentially S∗-compactness.


In this paper, a new notion of sequential compactness is introduced in L-topological spaces, which is called sequentially S∗-compactness. If L = [0, 1], sequential ultra-compactness, sequential N-compactness and sequential strong compactness imply sequential S∗-compactness, and sequential S∗-compactness implies sequential F-compactness. The intersection of a sequentially S∗-compact L-set and a closed L-set is sequentially S∗-compact. The continuous image of an sequentially S∗- compact L-set is sequentially S∗-compact. A weakly induced L-space (X, T ) is sequentially S∗-compact if and only if (X, [T ]) is sequential compact. The countable product of sequential S∗-compact L-sets is sequentially S∗-compact.

Biografía del autor/a

Shu-Ping Li, Mudanjiang Teachers College.
Department of Computer.


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

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

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

[4] Y.M. Liu, M.K. Luo, Fuzzy topology, World Scientific, Singapore, (1997).

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

[6] F.-G. Shi, A new notion of fuzzy compactness in L-fuzzy topological spaces, Information Sciences, in press.

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

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

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

[10] L.X. Xuan, Ultra-sequential compactness fts, countable ultra-
compact fts and ultra-subset compact fts, J. Mathematical Research and Exposition, 9, pp. 519—520, (1989). (in Chinese).

[11] L.X. Xuan, N-Sequential compactness, Fuzzy Sets and Systems, 35, pp. 93—100, (1990).

[12] L.X. Xuan, Countable strong compactness and strong sequential compactness, J. Nanjing Normal University, 2, pp. 14—19, (1989). (in Chinese).

[13] L.X. Xuan, Fuzzy sequential compactness, countable fuzzy compactness, Fuzzy Systems and Mathematics, 1, pp. 35—41, (1990). (in Chinese).
Cómo citar
Li, S.-P. (2017). Sequential S∗-compactness in L-topological spaces. Proyecciones. Journal of Mathematics, 24(1), 1-11.