Some separation axioms in L-topological spaces

  • Cuimei Jiang Qingdao Technological University.
  • Jin-Ming Fang Qingdao Technological University.
Palabras clave: L-topology, sub-separation axioms, sub-T1, sub-T2, sub-T2 1/2, sub-T3, sub-T4, L-topología, axiomas de sub-separación.

Resumen

In this paper, under the idea of L-Tq 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.

Biografía del autor/a

Jin-Ming Fang, Qingdao Technological University.
Department of Mathematics.

Citas

[1] C. L. Chang, Fuzzy topological spaces, J. Math.Anal. Appl., 24, pp.
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).‏
Publicado
2012-06-18
Cómo citar
Jiang, C., & Fang, J.-M. (2012). Some separation axioms in L-topological spaces. Proyecciones. Journal of Mathematics, 31(2), 125-147. https://doi.org/10.4067/S0716-09172012000200003
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Artículos