A new form of fuzzy β-compactness

  • Fu-Gui Shi Beijing Institute of Technology.
Palabras clave: L-topology, Compactness, β-compactness, Countable β-compactness, The β-Lindelöf property.


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-Lindel¨of property are also researched. 

Biografía del autor/a

Fu-Gui Shi, Beijing Institute of Technology.
Department of Mathematics.


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

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

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

[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).

[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).

[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).

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

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

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

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

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

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

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

[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).

[15] G.J. Wang, Theory of L-fuzzy topological space, Shaanxi Normal University Publishers, Xian, 1988. (in Chinese).
Cómo citar
Shi, F.-G. (2017). A new form of fuzzy β-compactness. Proyecciones. Journal of Mathematics, 24(2), 105-119. https://doi.org/10.4067/S0716-09172005000200002