SPN-compactness in L-topological spaces
DOI:
https://doi.org/10.4067/S0716-09172006000100004Keywords:
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.Abstract
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.References
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[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).
Published
2017-05-08
How to Cite
[1]
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.
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