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THE URYSOHN AXIOM AND THE COMPLETELY HAUSDORFF AXIOM IN L-TOPOLOGICAL SPACES | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 4، دوره 7، شماره 1، اردیبهشت 2010، صفحه 33-45 اصل مقاله (231.13 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2010.159 | ||
نویسندگان | ||
Fu-Gui Shi* ؛ Peng Chen | ||
Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing, 100081, P. R. China | ||
چکیده | ||
In this paper, the Urysohn and completely Hausdorff axioms in general topology are generalized to L-topological spaces so as to be compatible with pointwise metrics. Some properties and characterizations are also derived | ||
مراجع | ||
[1] S. L. Chen,Fuzzy Urysohn spaces and $\alpha$-stratified fuzzy Urysohn spaces, Proceedings of the Fifth IFSA World Congress I, Korea, (1993), 453-456. [2] S. L. Chen and Z. X.Wu,Urysohn separation property in topological molecular lattices, Fuzzy Sets and Systems,123(2) (2001), 177-184. [3] Z. Deng,Fuzzy pseudo-metric space, J. Math. Anal. Appl., 86 (1982), 74-95. [4] P. Dwinger,Characterizations of the complete homomorphic images of a completely distributive complete lattice I, Indagationes Mathematicae (Proceedings), 85 (1982), 403-414. [5] M. A. Erceg,Metric space in fuzzy set theory, J. Math. Anal. Appl., 69 (1979), 205-230. [6] J. Fang,H()-completely Hausdorff axiom on L-topological spaces, Fuzzy Sets and Systems, 140(3)(2003), 475-469. [7] J. Fang and Y. Yue,Urysohn closedness on completely distributive lattices, Fuzzy Sets and Systems,144(3) (2004), 367-381. [8] M. H. Ghanim, O. A. Tantawy and F. M. Selim,On lower separation axioms, Fuzzy Sets and Systems,85(3) (1997), 385-389. [9] G. Gierz and et al.,A compendium of continuous lattices, Springer Verlag, Berlin, 1980. [10] U. H¨ohle, S. E. Rodabaugh and eds,Mathematics of fuzzy sets: logic, topology and measure theory, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers (Boston/Dordrecht/London),3 (1999). [11] C. Hu,Fuzzy topological space, J. Math. Anal. Appl., 110 (1985), 141-178. [12] B. Hutton,Uniformities on fuzzy topological spaces, J. Math. Anal. Appl., 58 (1977), 559-571. [13] B. Hutton,Normality in fuzzy topological spaces, J. Math.Anal.Appl., 50 (1975), 74-79. [14] B. Hutton and I. Reilly,Separation axioms in fuzzy topological spaces, Fuzzy Sets and Systems, 3(1)(1980), 93-104. [15] O. Kaleva and S. Seikkala,On fuzzy metric spaces, Fuzzy Sets and Systems, 12(3) (1984), 215-229. [16] I. Kramosil and J. Michalek,Fuzzy metric and statistical metric spaces, Kybernetica, 11(1975), 326-334. [17] W. Kotz´e,Lifting of sobriety concepts with particular reference to (L,M)-topological spaces, in S. E. Rodabaugh, E. P. Klement and eds., Topological and Algebraic Structures in Fuzzy Sets, Kluwer Academic, Publishers (Boston/Dordrecht/London), 2003. [18] T. Kubiak,On L-Tychonoff spaces, Fuzzy Sets and Systems, 73(1) (1995), 25-53. [19] S. G. Li,H($\lambda$)-completely regular L-fuzzy sets and their applications, Fuzzy Sets and Systems, 95(2)(1998), 223-231 [20] S. G. Li,Separation axioms in L-fuzzy topological spaces (I): T0 and T1, Fuzzy Sets and Systems,116(3) (2000), 377-383. [21] Y. M. Liu and M. K. Luo,Pointwise characterizations of complete regularity and embedding theorem in fuzzy topological spaces, Science in China Ser. A, 26 (1983), 138-147. [22] Y. M. Liu and M. K. Luo,Fuzzy topology, World Scientific Publishing, Singapore, 1997. [23] R. Lowen and A. K. Srivastava,Sierpinski objects in subcategories of FTS, Quaestiones Mathematicae,11 (1988), 181-193. [24] R. Lowen and A. K. Srivastava,FTS0: the epireflective hull of the Sierpinski object in FTS, Fuzzy Sets and Systems,29(2) (1989), 171-176. [25] P. M. Pu and Y. M. Liu,Fuzzy topology I, neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571-599. [26] A. Pultr and S. E. Rodabaugh,Lattice- valued frames, functor categories and classes of sober spaces, in S. E. Rodabaugh, E. P. Klement and eds., Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic, Kluwer Academic Publishers (Boston/Dordrecht/London),20 (2003), 153-187. [27] A. Pultr and S. E. Rodabaugh,Examples for different sobrieties in fixed-basis topology, in S. E. Rodabaugh, E. P. Klement and eds., Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic, Kluwer Academic Publishers (Boston/Dordrecht/London),20 (2003), 427-440. [28] S. E. Rodabaugh,The Hausdorff separation axiom for fuzzy topological spaces, Topology and its Applications,11 (1980), 319-334. [29] S. E. Rodabaugh,Separation axioms and the L-fuzzy real lines, Fuzzy Sets and Systems, 11(2)(1983), 163-183. [30] S. E. Rodabaugh,A point-set lattice-theoretic framework T for topology which contains LOC as a subcategory of singleton subspaces and in which there are general classes of stone representation and compactification theorems, First Printing February 1986, Second Printing April 1987, Youngstown State University Printing Office, Youngstown, Ohio, USA. [31] S. E. Rodabaugh,Point-set lattice-theoretic topology, Fuzzy Sets and Systems, 40(2) (1991), 297-345. [32] S. E. Rodabaugh,Categorical frameworks for Stone representation theories, in S. E. Rodabaugh, E. P. Klement, U. H¨ohle and eds., Applications of Category Theory to Fuzzy Subsets, Theory and Decision Library: Series B: Mathematical and Statistical Methods, Kluwer Academic Publishers (Boston/Dordrecht/London),14 (1992), 177-231. [33] S. E. Rodabaugh,Applications of localic separation axioms, compactness axioms, representations and compactifications to poslat topological spaces, Fuzzy Sets and Systems, 73(1) (1995), 55-87. [34] S. E. Rodabaugh,Separation axioms: representation theorems, compactness and compactifications, in U. H¨ohle, S. E. Rodabaugh and eds., Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Boston, Dordrecht, London,3 (1999), 481-552. [35] F. G. Shi and L. J. Zhao,Pointwise characterizations of HR-regularity, J. Harbin Sci. Technol. Univ., in Chinese,1 (1995), 84-85. [36] F. G. Shi,Pointwise uniformities in L-fuzzy set theory, Fuzzy Sets and Systems, 98(1)(1998), 141-146. [37] F. G. Shi,Fuzzy pointwise complete regularity and imbedding theorem, J. Fuzzy Math., 2(1999), 305-310. [38] F. G. Shi,L-fuzzy pointwise metric spaces and T2 axiom, J. Capital Normal University, in Chinese,1 (2000), 8-12. [39] F. G. Shi,Pointwise pseudo-metrics in L-fuzzy set theory, Fuzzy Sets and Systems, 121(2) (2001),209-216. [40] F. G. Shi and C. Y. Zheng,Metrization theorems in L-topological spaces, Fuzzy Sets and Systems,149(3) (2005), 455-471. [41] F. G. Shi,A new notion of fuzzy compactness in L-topological spaces, Information Sciences, 173(2005), 35-48. [42] F. G. Shi,Pointwise pseudo-metric on the L-real line, Iranian Journal of Fuzzy Systems, 2(2)(2005), 15-20. [43] F. G. Shi,A new approach to L-T2, L-Urysohn and L-completely hausdorff axioms, Fuzzy Sets and Systems,157(6) (2006), 794-803. [44] G. J. Wang,Theory of topological molecular lattices, Fuzzy Sets and Systems, 47(3) (1992), 351-376. [45] G. J. Wang,Theory of L-fuzzy topological spaces, Shaanxi Normal University Press, Xi’an, 1988. [46] M. D. Weiss,Fixed points, separation and induced topologies for fuzzy sets, J. Math. Anal. Appl.,50 (1975), 142-150. [47] P. Wuyts and R. Lowen,On local and global measures of separation in fuzzy topological spaces, Fuzzy Sets and Systems, 19(1) (1986), 51-80. [48] D. Zhang and Y. Liu,Weakly induced modifications of L-fuzzy topological spaces, Acta Math. Sinica,36 (1993), 68-73. | ||
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