## Services on Demand

## Journal

## Article

## Indicators

- Cited by SciELO
- Access statistics

## Related links

- Cited by Google
- Similars in SciELO
- Similars in Google

## Share

## Proyecciones (Antofagasta)

##
*Print version* ISSN 0716-0917

### Proyecciones (Antofagasta) vol.31 no.2 Antofagasta June 2012

#### http://dx.doi.org/10.4067/S0716-09172012000200003

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-*T2**1 ***;sub-T3;sub-T4.*

**REFERENCES**

[1] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24, pp. 182190, (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. 16, (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. 359366, (1998).

[4] M. Gu, B. Zhao, Layer separation axioms in L-fuzzy topological spaces, Fuzzy Systems and Mathematics, 17, pp. 1218 (in Chinese), (2003).

[5] S. Ganguly and S. Saha, On separation axioms and T¿-fuzzy continuity, Fuzzy Sets and Systems, 16, pp. 265275, (1985).

[6] B. Hutton, Normality in fuzzy topoligical spaces, J. Math. Anal. Appl., 50, pp. 7479, (1975).

[7] T. Kubiak, On L-Tychonoff spaces, Fuzzy Sets and Systems, 73, pp. 2553, (1995).

[8] A. Kandil, M.E. El-Shafee, Regularity axioms in fuzzy topological spaces and FR¿-proximities, Fuzzy Sets and Systems, 27, pp. 217231, (1988).

[9] Y. Liu, Pointwise characterizations of complete regularity and embe-ding thorem in fuzzy topological space, Sci. Sinica. Ser. A 26, pp. 138147, (1983).

[10] Y. Liu, M. Luo, Separation in latticed induced spaces, Fuzzy Sets and Systems, 36, pp. 5566, (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. 621633, (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. 177231, (1992).

[14] F. G. Shi, A new approach to L-T2, L-Urysohn, and L-completely Hausdorff axioms, Fuzzy Sets and Systems, 157, pp. 794803, (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. 316328, (1974).

[18] P. Wuyts, R. Lowen, On local and global measures of separation in fuzzy topological spaces, Fuzzy Sets and Systems, 19, pp. 5180, (1986).

[19] F. You, The separation axioms of T2| L-fts and ST2 2 L-fts, Fuzzy Systems and Mathematics, 15, pp. 7376 (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 :