Liang, C., Shi, F. (2015). The Urysohn, completely Hausdorff and completely regular axioms in $L$-fuzzy topological spaces. Iranian Journal of Fuzzy Systems, 12(6), 109-128. doi: 10.22111/ijfs.2015.2183
Chengyu Liang; Fu-Gui Shi. "The Urysohn, completely Hausdorff and completely regular axioms in $L$-fuzzy topological spaces". Iranian Journal of Fuzzy Systems, 12, 6, 2015, 109-128. doi: 10.22111/ijfs.2015.2183
Liang, C., Shi, F. (2015). 'The Urysohn, completely Hausdorff and completely regular axioms in $L$-fuzzy topological spaces', Iranian Journal of Fuzzy Systems, 12(6), pp. 109-128. doi: 10.22111/ijfs.2015.2183
Liang, C., Shi, F. The Urysohn, completely Hausdorff and completely regular axioms in $L$-fuzzy topological spaces. Iranian Journal of Fuzzy Systems, 2015; 12(6): 109-128. doi: 10.22111/ijfs.2015.2183
The Urysohn, completely Hausdorff and completely regular axioms in $L$-fuzzy topological spaces
1College of Science, North China University of Technology, No.5 Jinyuanzhuang Road, Shijingshan District, 100144 Beijing, P.R. China
2School of Mathematics and Statistics, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, 100081 Beijing, P.R. China
Abstract
In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular to some degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.
[1] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182–190. [2] S. L. Chen and Z. X.Wu, Urysohn separation property in topological molecular lattices, Fuzzy Sets Syst., 123 (2001), 177–184. [3] P. Dwinger, Characterizations of the complete homomorphic images of a completely distributive complete lattice I, Indagationes Mathematicae(Proceedings), 85 (1982), 403–414. [4] J. M. Fang, H()-completely Hausdorff axiom on L-topological spaces, Fuzzy Sets Syst., 140 (2003), 475–469. [5] J. M. Fang and Y. L. Yue, Urysohn closedness on completely distributive lattices, Fuzzy Sets Syst., 144 (2004), 367–381. [6] J. M. Fang and Y. L. Yue, Base and subbase in I-fuzzy topological spaces, J. Math. Res. Exposition, 26 (2006), 89–95. [7] G. Gierz, et al., A compendium of continuous lattices, Springer Verlag, Berlin, 1980. [8] B. Hutton, Normality in fuzzy topological spaces, J. Math. Anal. Appl., 50 (1975), 74–79. [9] U. H¨ohle, Probabilistic metrization of fuzzy uniformities, Fuzzy Sets Syst., 8 (1982), 63–69. [10] U. H¨ohle and A. P. ˘Sostak, Axiomatic foudations of fixed-basis fuzzy topology, In: U. H¨ohle, S. E. Rodabaugh(Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Handbook Series, vol.3, Kluwer Academic Publishers, Boston, Dordrecht, London, (1999), 123–173. [11] T. Kubiak, On fuzzy topologies, Ph. D. Thesis, Adam Mickiewicz, Poznan, Poland, 1985. [12] H. Y. Li and F. G. Shi, Some separation axioms in I-fuzzy topological spaces, Fuzzy Sets Syst., 159 (2008), 573–587. [13] S. E. Rodabaugh, The Hausdorff separation axiom for fuzzy topological spaces, Topology Appl., 11 (1980), 319–334. [14] F. G. Shi, Pointwise uniformities and pointwise metrics on fuzzy lattices, Chinese Science Bulletin, 42 (1997), 718–720. [15] F. G. Shi, Pointwise uniformities in fuzzy set theory, Fuzzy Sets Syst., 98 (1998), 141-146. [16] F. G. Shi, Fuzzy pointwise complete regularity and imbedding theorem, The Journal of Fuzzy Mathematics, 7 (1999), 305–310. [17] F. G. Shi, A new approach to L-T2, L-Urysohn, and L-completely Hausdorff axioms, Fuzzy Sets Syst., 157 (2006), 794–803. [18] F. G. Shi, The Urysohn axiom and the completely Hausdorff axiom in L-topological spaces, Iranian Journal of Fuzzy Systems, 7(1) (2010), 33–45. [19] F. G. Shi, (L;M)-fuzzy metric spaces, Indian J. Math., 52 (2010), 231-250. [20] F. G. Shi, Regularity and normality of (L;M)-fuzzy topological spaces, Fuzzy Sets Syst., 182 (2011), 37–52. [21] A. P. ˇSostak, On a fuzzy topological structure, Suppl. Rend. Circ. Mat. PalermoSer. II, 11 (1985), 89–103. [22] A. P. ˇSostak, Two decades of fuzzy topology: basic ideas, notions and results, Russian Math. Surveys, 44 (1989), 125–186. [23] M. Ying, A new approach to fuzzy topology (I), Fuzzy Sets Syst., 39 (1991), 303–321.
[24] Y. L. Yue and J. M. Fang, Generated I-fuzzy topological spaces, Fuzzy Sets Syst., 154 (2005), 103–117. [25] Y. L. Yue and J. M. Fang, On separation axioms in I-fuzzy topological spaces, Fuzzy Sets Syst., 157 (2006), 780–793.
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