Countable s*-compactness in L-spaces

Gui-Qin Yang

Resumen


In this paper, the notions of countable S∗-compactness is introduced in L-topological spaces based on the notion of S∗-compactness. An S∗-compact L-set is countably S∗-compact. If L = [0, 1], then countable strong compactness implies countable S∗-compactness and countable S∗-compactness implies countable F-compactness, but each inverse is not true. The intersection of a countably S∗-compact L-set and a closed L-set is countably S∗-compact. The continuous image of a countably S∗-compact L-set is countably S∗-compact. A weakly induced L-space (X, T ) is countably S∗-compact if and only if (X, [T ]) is countably compact.


Palabras clave


L-topology ; βa-open cover ; Qa-open cover ; S∗-compactness ; countable S∗-compactness.

Texto completo:

PDF

Referencias


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, Indagationes Mathematicae (Proceedings) 85, pp. 403—414, (1982).

T. E. Gantner, R. C. Steinlage and R.H. Warren, Compactness in fuzzy topological spaces, J.Math. Anal. Appl. 62, pp. 547-562, (1978).

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, pp. 734—742, (1973).

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

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

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, pp. 621-633, (1976).

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

G. W. Meng, Countable N-compactness in L-fuzzy topological spaces, Fuzzy Systems and Mathematics. add, pp. 234—238, (1992).

F.-G. Shi, G.-Q. Yang, Countable fuzzy compactness in L-topological spaces, J. Harbin Univ. Sci. & Tech. 2, pp. 499—507, (1992).

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

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. A new notion of fuzzy compactness in L-topological spaces, Information Sciences 173, pp. 35—48, (205), (2005).

G.-J. Wang, A new fuzzy compactness defined by fuzzy nets, J.

Math. Anal. Appl. 94, pp. 1—23, (1983).

G.-J. Wang, Theory of L-fuzzy topological space, Shanxi Normal University Press, Xi’an, (1988). (in Chinese).

C. K. Wong, Covering properties of fuzzy topological spaces, J. Math. Anal. Appl. 43, (1973), pp. 697—704.

L. X. Xuan, Countable strong compactness and strong sequential compactness, J. Nanjing Normal Unifersity 2, pp. 14—19, (1989).

L. X. Xuan, Countable ultra-compactness and ultra-sequential compactness, J. Mathematical Research and Exposition 9, pp. 519—520, (1989)

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




DOI: http://dx.doi.org/10.4067/S0716-09172005000300007

Enlaces refback

  • No hay ningún enlace refback.