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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/S0716-09172005000200002 

 

Proyecciones
Vol. 24, No 2, pp. 105-119, August 2005.
Universidad Católica del Norte
Antofagasta - Chile

 

A NEW FORM OF FUZZY β-COMPACTNESS*

 

FU - GUI SHI

Beijing Institute of Technology, China

Correspondencia a :


ABSTRACT

A new form of β-compactness is introduced in L-topological spaces by means of β-open L-sets and their inequality where L is a complete de Morgan algebra. This new form doesn’t rely on the structure of basis lattice L. It can also be characterized by means of β-closed L-sets and their inequality. When L is a completely distributive de Morgan algebra, its many characterizations are presented. Meanwhile countable β-compactness and the β-Lindelöf property are also researched.

KeyWords and Phrases: L-topology, compactness, β-compactness, countable β-compactness, the β-Lindelöf property

Mathematics Subject Classification (2000): 54A40, 54D30, 54A20

Dedicatory : Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China


 

REFERENCES

[1] M. A. Fath Alla, On fuzzy topological spaces, Ph. D. Thesis, Assiut Univ., Sohag, Egypt (1984).        [ Links ]

[2] G. Balasubramanian, On fuzzy β-compact spaces and fuzzy β- extremally disconnected spaces, Kybernetika [cybernetics] 33, pp. 271—277, (1997).        [ Links ]

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

[4] 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 ]

[5] M. E. A. El-Monsef, S.N. El-Deeb and R.A. Mahmoud, β-open sets and β-continuous mappings, Bull. Fac. Sci., Assiut Univ., 12, pp. 77—90, (1983).        [ Links ]

[6] M. E. A. El-Monsef and A.M. Kozae, Some generalized forms of compactness and closedness, Delta J. Sci. 9(2), pp. 257—269, (1985).        [ Links ]

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

[8] I. M. Hanafy, Fuzzy β-compactness and fuzzy β-closed spaces, Turk J. Math., 28, pp. 281—293, (2004).        [ Links ]

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

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

[11] M. K. Singal and N. Prakash, Fuzzy preopen sets and fuzzy preseparation axioms, Fuzzy Sets and Systems, 44, pp. 273—281, (1991).        [ Links ]

[12] F.-G. Shi, Fuzzy compactness in L-topological spaces, submitted.        [ Links ]

[13] F.-G. Shi, Countable compactness and the Lindelöf property of L-fuzzy sets, Iranian Journal of Fuzzy Systems, 1, pp. 79—88, (2004).        [ Links ]

[14] F.-G. Shi, Theory of Lβ-nest sets and Lα-nest sets and their applications, Fuzzy Systems and Mathematics, 4, pp. 65—72, (1995) (in Chinese).        [ Links ]

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

Received : March 2005. Accepted : July 2005

*This work 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
Beijing Insitut of Technology
Beijing 100081
P. R. China
China
E-mail: fuguishi@bit.edu.cn or f.g.shi@263.net

 

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