Proyecciones Journal of Mathematics Vol. 31, N^o 2, pp. 125-147, June 2012. Universidad Católica del Norte Antofagasta - Chile

 

Some separation axioms in L-topological spaces

 

Cui-Mei Jiang*, Jin-Ming Fang**

* Qingdao Tecnological University, China

** Ocean University of China, China

---

ABSTRACT

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.

Keywords : L-topology; sub-separation axioms; sub-T\;sub-T2;sub-T21 ;sub-T3;sub-T4.

---

REFERENCES

[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 topo-logical 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 T¿-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 FR¿-proximities, Fuzzy Sets and Systems, 27, pp. 217—231, (1988).

[9] Y. Liu, Pointwise characterizations of complete regularity and embe-ding 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 Haus-dorff 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| L-fts and ST2 2 L-fts, Fuzzy Systems and Mathematics, 15, pp. 73—76 (in Chinese), (2001).

---

Received : December 2011. Accepted : January 2012

Cui-Mei Jiang

Qingdao Technological University

11 Fushun Road Qingdao 266033

P. R. China

China

e-mail : jiangcuimei2004@163.com

 

Jin-Ming Fang

Department of Mathematics

Ocean University of China

China

e-mail :