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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.24 n.2 Antofagasta ago. 2005

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

 

Proyecciones
Vol. 24, No 2, pp. 153-165, August 2005.
Universidad Católica del Norte
Antofagasta - Chile

 

Sβ−COMPACTNESS IN L-TOPOLOGICAL SPACES*

 

FU - GUI SHI

Beijing Institute of Technology, China

Correspondencia a :


ABSTRACT

In this paper, the notion of Sβ−compactness is introduced in Ltopological spaces by means of open βα−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.

Math. Subject Classification : 54A40

KeyWords and Phrases : L-topology, βα−cover, Sβ−compactness, β−cluster point


 

REFERENCES

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

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

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

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

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

[6] 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. Höhle, eds., 1992, Kluwer Academic Publishers, 275—305.        [ Links ]

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

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

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

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

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

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

[13] 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).        [ Links ]

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

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

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

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

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

Received : May 2005. Accepted : August 2005

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

Fu-Gui Shi

Department of Mathematics
School of Science
Beijing Institute of Technology
Beijing 100081
P.R. China
e-mail : fuguishi@bit.edu.cn or f.g.shi@263.net

 

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