SPN-compactness in L-topological spaces


  • Zhen-Guo Xu Beijing Institute of Technology.
  • Fu-Gui Shi Beijing Institute of Technology.




L-topological space, strongly preopen L-set, strongly preclosed L-set, SPN-compactness, countable SPN-compactness, the SPN-Lindel of property, espacio L-topológico, L-conjunto fuertemente pre-abierto, L-conjunto fuertemente pre-cerrado, SPN-compacidad.


In this paper, the notions of SPN-compactness, countable SPNcompactness and the SPN-Lindelöf property are introduced in L-topological spaces by means of strongly preclosed L-sets. In an L-space, an Lset having the SPN-Lindelöf property is SPN-compact if and only if it is countably SPN-compact. (Countable) SPN-compactness implies (countable) N-compactness, the SPN-Lindelöf property implies the N-Lindelöf property, but each inverse is not true. Every L-set with finite support is SPN-compact. The intersection of an (a countable) SPN-compact L-set and a strongly preclosed L-set is (countably) SPNcompact. The strong preirresolute image of an (a countable) SPNcompact L-set is (countably) SPN-compact. Moreover SPN-compactness can be characterized by nets.

Author Biographies

Zhen-Guo Xu, Beijing Institute of Technology.

Department of Mathematics.

Fu-Gui Shi, Beijing Institute of Technology.

Department of Mathematics.


[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] B. Krateska, Fuzzy strongly preopen sets and fuzzy strong precontinuity, Matematicki Vesnik, 50, pp. 111—123, (1998).

[7] B. Krateska, Some fuzzy SP-topological properties, Matematicki Vesnik, 51, pp. 39—51, (1999).

[8] S.R.T. Kudri, Compactness in L-topological spaces, Fuzzy Sets and Systems, 67, pp. 329—336, (1994).

[9] S.-G. Li, et al., Strong fuzzy compact sets and ultra-fuzzy compact sets in L-spaces, Fuzzy Sets and Systems, 147, pp. 293—306, (2004).

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

[11] Y.-M. Liu, M.K. Luo, Fuzzy topology, World Scientific, Singapore, 1997.

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

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

[14] F.-G. Shi, et al., Characterizations and properties of countably Ncompact sets, J. of Math (PRC), 21, pp. 429—432, (2001).

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

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

[17] F.-G. Shi, A new form of fuzzy ß-compactness, Proyecciones Journal of Mathematics, 24, pp. 105—119, (2005)

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

[19] G.-J. Wang, Theory of L-fuzzy topological spaces, Shaanxi Normal University Press, Xian, (in Chinese), (1988)

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

[21] D.-S. Zhao, The N-compactness in L-fuzzy topological spaces, J. Math. Anal. Appl., pp. 128, pp 64—79, (1987).



How to Cite

Z.-G. Xu and F.-G. Shi, “SPN-compactness in L-topological spaces”, Proyecciones (Antofagasta, On line), vol. 25, no. 1, pp. 47-61, May 2017.