versión impresa ISSN 0716-0917
Proyecciones (Antofagasta) v.24 n.1 Antofagasta mayo 2005
SEQUENTIAL S*-COMPACTNESS IN L-TOPOLOGICAL SPACES*
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.
Key Words and Phrases: L-topology, constant a-sequence, weak O-cluster point, weak O-limit point, sequentially S*-compactness
2000 Math. Subject Classification: Primary: 54A40.
 C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24, pp.182190, (1968). [ Links ]
 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). [ Links ]
 G. Gierz, et al., A compendium of continuous lattices, Springer Verlag, Berlin, (1980). [ Links ]
 Y.M. Liu, M.K. Luo, Fuzzy topology, World Scientific, Singapore, (1997). [ Links ]
 R. Lowen, A comparision of di.erent compactness notions in fuzzy topological spaces, J. Math. Anal. Appl., 64, pp. 446454, (1978). [ Links ]
 F.-G. Shi, A new notion of fuzzy compactness in L-fuzzy topological spaces, Information Sciences, in press. [ Links ]
 F.-G. Shi, C.-Y. Zheng, O-convergence of fuzzy nets and its applications, Fuzzy Sets and Systems, 140, pp. 499507, (2003). [ Links ]
 G.J. Wang, A new fuzzy compactness defined by fuzzy nets, J. Math. Anal. Appl., 94, pp. 123, (1983). [ Links ]
 G.J. Wang, Theory of L-fuzzy topological space, Shaanxi Normal University Press, Xian, 1988. (in Chinese). [ Links ]
 L.X. Xuan, Ultra-sequential compactness fts, countable ultra-compact fts and ultra-subset compact fts, J. Mathematical Research and Exposition, 9, pp. 519520, (1989). (in Chinese). [ Links ]
 L.X. Xuan, N-Sequential compactness, Fuzzy Sets and Systems, 35, pp. 93100, (1990). [ Links ]
 L.X. Xuan, Countable strong compactness and strong sequential compactness, J. Nanjing Normal University, 2, pp. 1419, (1989). (in Chinese). [ Links ]
 L.X. Xuan, Fuzzy sequential compactness, countable fuzzy compactness, Fuzzy Systems and Mathematics, 1, pp. 3541, (1990). (in Chinese). [ Links ]
Received : January 2005, Accepted : March 2005.