A new form of fuzzy β-compactness

Fu-Gui Shi


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. 

Palabras clave

L-topology ; Compactness ; β-compactness ; Countable β-compactness ; The β-Lindelöf property.

Texto completo:



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

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

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

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).

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).

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).

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

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

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

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

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

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

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

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).

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

DOI: http://dx.doi.org/10.4067/S0716-09172005000200002

Enlaces refback

  • No hay ningún enlace refback.