Sequential S∗-compactness in L-topological spaces

Shu-Ping Li


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.

Palabras clave

L-topology ; Constant a-sequence ; Weak O-cluster point ; Weak O-limit point ; Sequentially S∗-compactness.

Texto completo:



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

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).

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

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

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

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

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

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

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

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).

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

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

L.X. Xuan, Fuzzy sequential compactness, countable fuzzy compactness, Fuzzy Systems and Mathematics, 1, pp. 35—41, (1990). (in Chinese).


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