Countable s*-compactness in L-spaces

  • Gui-Qin Yang Mudanjiang Teachers College.
Palabras clave: L-topology, βa-open cover, Qa-open cover, S∗-compactness, countable S∗-compactness.

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.

Biografía del autor/a

Gui-Qin Yang, Mudanjiang Teachers College.
Department of Mathematics.

Citas

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

[2] P. Dwinger, Characterizations of the complete homomorphic images of a completely distributive complete lattice I, Indagationes Mathematicae (Proceedings) 85, pp. 403—414, (1982).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[21] D. S. Zhao,The N-compactness in L-fuzzy topological spaces, J. Math. Anal. Appl. 128, pp. 64—70, (1987).
Publicado
2017-04-20
Cómo citar
Yang, G.-Q. (2017). Countable s*-compactness in L-spaces. Proyecciones. Journal of Mathematics, 24(3), 287-294. https://doi.org/10.4067/S0716-09172005000300007
Sección
Artículos