Some separation axioms in L-topological spaces
DOI:
https://doi.org/10.4067/S0716-09172012000200003Keywords:
L-topology, sub-separation axioms, sub-T1, sub-T2, sub-T2 1/2, sub-T3, sub-T4, L-topología, axiomas de sub-separación.Abstract
In this paper, under the idea of L-T0 or sub-T0,we propose a set of new separation axioms in L-topological spaces, namely sub-separation axioms. And some of their properties are studied. In addition, the relation between the sub-separation axioms defined in the paper and other separation axioms is discussed. The results show that the sub-separation axioms in this paper are weaker than other separation axioms that had appeared in literature.References
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138—147, (1983).
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[12] R. Lowen, Fuzzy topological spaces and compactness, J. Math. Anal. Appl., 56, pp. 621—633, (1976).
[13] S. E. Rodabaugh, Categorical frameworks for stone representation theorems, in: S. E. Rodabaugh, et al., (Eds.), Applications of category theory to Fuzzy Subsets, Kluwer Academic Publishers, Netherlands, pp. 177—231, (1992).
[14] F. G. Shi, A new approach to L-T2, L-Urysohn, and L-completely Hausdorff axioms, Fuzzy Sets and Systems, 157, pp. 794—803, (2006).
[15] F. G. Shi and P. Chen, The Urysohn axiom and the completely Hausdorff axiom in L-topological spaces, Iranian Journal of Fuzzy Systems, Vol. 7, No. 1, pp. 33-45, (2010).
[16] G. Wang, Theory of L-fuzzy topolgical spaces, Sha’anxi Normal University Xi’an, (1988) (in Chinese).
[17] C. K. Wong, Fuzzy point and local properties of fuzzy topology, J. Math. Anal. Appl., 46, pp. 316—328, (1974).
[18] P. Wuyts, R. Lowen, On local and global measures of separation in fuzzy topological spaces, Fuzzy Sets and Systems, 19, pp. 51—80, (1986).
[19] F. You, The separation axioms of T2 1 2 L-fts and ST2 1 2 L-fts, Fuzzy Systems and Mathematics, 15, pp. 73—76 (in Chinese), (2001).
182—190, (1968).
[2] S. L. Chen, G. W. Meng, U-separation axioms and characterizations in L-fuzzy topological spaces, J. Liaochen. Sci. Technol. Univ., 11(1), pp. 1—6, (1998).
[3] J.X. Fang, B. Ren, A set of new separation axioms in L-fuzzy topological spaces, Fuzzy sets and systems, 96, pp. 359—366, (1998).
[4] M. Gu, B. Zhao, Layer separation axioms in L-fuzzy topological spaces, Fuzzy Systems and Mathematics, 17, pp. 12—18 (in Chinese), (2003).
[5] S. Ganguly and S. Saha, On separation axioms and Ti-fuzzy continuity, Fuzzy Sets and Systems, 16, pp. 265—275, (1985).
[6] B. Hutton, Normality in fuzzy topoligical spaces, J. Math. Anal. Appl., 50, pp. 74—79, (1975).
[7] T. Kubiak, On L-Tychonoff spaces, Fuzzy Sets and Systems, 73, pp.
25—53, (1995).
[8] A. Kandil, M.E. El-Shafee, Regularity axioms in fuzzy topological spaces and FRi-proximities, Fuzzy Sets and Systems, 27, pp. 217—231, (1988).
[9] Y. Liu, Pointwise characterizations of complete regularity and embeding thorem in fuzzy topological space, Sci. Sinica. Ser. A 26, pp.
138—147, (1983).
[10] Y. Liu, M. Luo, Separation in latticed induced spaces, Fuzzy Sets and Systems, 36, pp. 55—66, (1990).
[11] Y. Liu, M. Luo, Fuzzy topology, World Scienctific Publishing, Singapore, (1997).
[12] R. Lowen, Fuzzy topological spaces and compactness, J. Math. Anal. Appl., 56, pp. 621—633, (1976).
[13] S. E. Rodabaugh, Categorical frameworks for stone representation theorems, in: S. E. Rodabaugh, et al., (Eds.), Applications of category theory to Fuzzy Subsets, Kluwer Academic Publishers, Netherlands, pp. 177—231, (1992).
[14] F. G. Shi, A new approach to L-T2, L-Urysohn, and L-completely Hausdorff axioms, Fuzzy Sets and Systems, 157, pp. 794—803, (2006).
[15] F. G. Shi and P. Chen, The Urysohn axiom and the completely Hausdorff axiom in L-topological spaces, Iranian Journal of Fuzzy Systems, Vol. 7, No. 1, pp. 33-45, (2010).
[16] G. Wang, Theory of L-fuzzy topolgical spaces, Sha’anxi Normal University Xi’an, (1988) (in Chinese).
[17] C. K. Wong, Fuzzy point and local properties of fuzzy topology, J. Math. Anal. Appl., 46, pp. 316—328, (1974).
[18] P. Wuyts, R. Lowen, On local and global measures of separation in fuzzy topological spaces, Fuzzy Sets and Systems, 19, pp. 51—80, (1986).
[19] F. You, The separation axioms of T2 1 2 L-fts and ST2 1 2 L-fts, Fuzzy Systems and Mathematics, 15, pp. 73—76 (in Chinese), (2001).
Published
2012-06-18
How to Cite
[1]
C. Jiang and J.-M. Fang, “Some separation axioms in L-topological spaces”, Proyecciones (Antofagasta, On line), vol. 31, no. 2, pp. 125-147, Jun. 2012.
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