A new notion of SP-compact L-fuzzy sets
DOI:
https://doi.org/10.4067/S0716-09172006000300003Keywords:
L-topology, semi-preopen L-set, SP-compactness, L-topología, L-conjunto semi-preabierto, SP-compacidad.Abstract
A new notion of SP-compactness is introduced in L-topological spaces by means of semi-preopen L-sets and their inequality, where L is a complete De Morgan algebra. This new notion does not depend on the structure of basis lattice L and L does not require any distributivity. This new notion implies semicompactness, hence it also implies compactness. This new notion is a good extension and it has many characterizations if L is completely distributive De Morgan algebra.References
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[2] S.Z.Bai, L-fuzzy SP-compact sets, Advances in Mathematics, 33, pp.316-322, (2004).
[3] S.Z.Bai, Countably SP-compact subsets, Fuzzy Systems and Mathematics, 19, pp.59-61, (2005).
[4] C.L.Chang, Fuzzy topological spaces, J.Math.Anal.Appl. 24, pp.182-190, (1968).
[5] 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).
[6] G.Gierz, et al. A Compendium of Continuous Lattices, Springer Verlag, Berlin, (1980).
[7] Y.M.Liu, M.K.Luo, Fuzzy Topology, World Scienti.c, Singapore, (1998).
[8] F.G.Shi, Semicompactness in L-topological spaces, International Journal of Mathematics Mathematical Sciences, 12, pp.1869-1878, (2005).
[9] F.G.Shi, A new form of fuzzy ß-compactness, Proyecciones Journal of Mathematics, 24, pp.105-119, (2005).
[10] F.G.Shi, Fuzzy compactness in L-topological spaces, Acta Math.Sinica, submitted.
[11] S.S.Thakur, S.Singh, On fuzzy semi-preopen sets and fuzzy semiprecontinuity, Fuzzy Sets and Systems, 98, pp.383-391, (1998).
[12] G.J.Wang, Theory of L-Fuzzy Topological Space, Shaanxi Normal University Press, Xian, (1988).
Published
2017-05-08
How to Cite
[1]
S.-Z. Bai, “A new notion of SP-compact L-fuzzy sets”, Proyecciones (Antofagasta, On line), vol. 25, no. 3, pp. 249-259, May 2017.
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