Sβ−compactness in L-topological spaces

Fu-Gui Shi

Resumen


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


Palabras clave


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

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Referencias


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

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

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

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

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

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.

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

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

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

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

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

F.-G. Shi, A new form of fuzzy β-compactness, submitted to Proyecciones, 2005.

F.-G. Shi, Theory of Lβ-nested sets and Lα-nest sets and its applications, Fuzzy Systems and Mathematics 4(1995), 65—72 (in Chinese).

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

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

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

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

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




DOI: http://dx.doi.org/10.4067/S0716-09172005000200004

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