Proyecciones
Vol. 24, No 1, pp. 1-11, Mayo 2005.
Universidad Católica del Norte
Antofagasta - Chile

SEQUENTIAL S*-COMPACTNESS IN L-TOPOLOGICAL SPACES*

SHU-PING LI
Mudanjiang Teachers College, China.

Correspondencia a :

ABSTRACT

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.

References

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

[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).        [ Links ]

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

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

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

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

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

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

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

[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).        [ Links ]

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

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

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

Received : January 2005, Accepted : March 2005.

*The project is supported by National Natural Science Foundation of China(10371079) and Base Research Foundation of Beijing Institute of Technology.

Shu-Ping Li
Department of Computer
Mudanjiang Teachers College
Mudanjiang 157012, P.R. China
China
e-mail: lishuping46@hotmail.com