Browse > Article
http://dx.doi.org/10.4134/JKMS.2007.44.6.1383

L-FUZZY UNIFORM SPACES  

Yue, Yue-Li (DEPARTMENT OF MATHEMATICS OCEAN UNIVERSITY OF CHINA)
Shi, Fu-Gui (DEPARTMENT OF MATHEMATICS BEIJING INSTITUTE OF TECHNOLOGY)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.6, 2007 , pp. 1383-1396 More about this Journal
Abstract
The aim of this paper is to study L-fuzzy uniformizable spaces. A new kind of topological fuzzy remote neighborhood system is defined and used for investigating the relationship between L-fuzzy co-topology and L-fuzzy (quasi-)uniformity. It is showed that this fuzzy remote neighborhood system is different from that in [23] when $\mathcal{U}$ is an L-fuzzy quasi-uniformity and they will be coincident when $\mathcal{U}$ is an L-fuzzy uniformity. It is also showed that each L-fuzzy co-topological space is L-fuzzy quasi-uniformizable.
Keywords
L-fuzzy co-topology; fuzzy remote neighborhood system; L-fuzzy (quasi-)uniformity;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
1 G. Gierz, K. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove, and D. S. Scott, A compendium of continuous lattice, Springer, Berlin, 1980
2 T. Kubiak, On fuzzy topologies (PhD Thesis, Adam Mickiewicz, Poznan (Poland), 1985
3 R. Lowen, Fuzzy uniform spaces, J. Math. Anal. Appl. 82 (1981), no. 2, 370-385   DOI
4 S. E. Rodabaugh, A theory of fuzzy uniformities with applications to the fuzzy real lines, J. Math. Anal. Appl. 129 (1988), no. 1, 37-70   DOI
5 S. E. Rodabaugh, Powerset operator foundations for poslat fuzzy set theories and topologies, Handb. Fuzzy Sets Ser., 3, Kluwer Acad. Publ., Boston, MA, 1999
6 U. Hohle, Probabilistic topologies induced by L-fuzzy uniformities, Manuscripta Math. 38 (1982), no. 3, 289-323   DOI
7 J. Adamek, H. Herrlich, and G. E. Strecker, Abstract and Concrete Categories, J. Wiley & Sons, New York, 1990
8 D. Dzhajanbajev and A. P. .Sostak, On a fuzzy uniform structure, Tartu Ul. Toimetised No. 940 (1992), 31-36
9 J. Gutierrez Garcia, M. A. de Prada Vicente, and A. P. .Sostak, A unified approach to the concept of fuzzy L-uniform space, Trends Log. Stud. Log. Libr., 20, Kluwer Acad. Publ., Dordrecht, 2003
10 U. Hohle, Upper semicontinuous fuzzy sets and applications, J. Math. Anal. Appl. 78 (1980), no. 2, 659-673   DOI
11 U. HÄohle and A. P. .Sostak, Axiomatic foundations of fixed-basis fuzzy topology, Handb. Fuzzy Sets Ser., 3, Kluwer Acad. Publ., Boston, MA, 1999
12 B. Hutton, Uniformities on fuzzy topological spaces, J. Math. Anal. Appl. 58 (1977), no 3, 557-571   DOI
13 D. Zhang, A comparison of various uniformities in fuzzy topology, Fuzzy Sets and Systems 140 (2003), no. 3, 399-422   DOI   ScienceOn
14 C. Y. Kim, L-fuzzy quasi-uniformizable spaces, Indian J. Pure Appl. Math. 35 (2004), no. 5, 599-619
15 W. Kotze, Uniform spaces, Handb. Fuzzy Sets Ser., 3, Kluwer Acad. Publ., Boston, MA, 1999
16 Y. M. Liu and M. K. Luo, Fuzzy Topology, World Scientific, Singapore, 1997
17 S. E. Rodabaugh, Categorical foundations of variable-basis fuzzy topology, Handb. Fuzzy Sets Ser., 3, Kluwer Acad. Publ., Boston, MA, 1999
18 S. E. Rodabaugh,, Axiomatic foundations for uniform operator quasi-uniformities, Trends Log. Stud. Log. Libr., 20, Kluwer Acad. Publ., Dordrecht, 2003
19 F. G. Shi, Pointwise uniformities in fuzzy set theory, Fuzzy Sets and Systems 98 (1998), no. 1, 141-146   DOI   ScienceOn
20 F. G. Shi, J. Zhang, and C. Y. Zheng, L-proximities and totally bounded pointwise L-uniformities, Fuzzy Sets and Systems 133 (2003), no. 3, 321-331   DOI   ScienceOn
21 A. P. .Sostak, On a fuzzy topological structure, Rend. Circ. Mat. Palermo (2) Suppl. No. 11 (1985), 89-103
22 A. P. Sostak, Basic structures of fuzzy topology, J. Math. Sci. 78 (1996), no. 6, 662-701   DOI
23 D. Zhang, Stratified Hutton uniform spaces, Fuzzy Sets and Systems 130 (2002), no. 3, 337-346   DOI   ScienceOn
24 Y. Yue and J. Fang, Categories isomorphic to the Kubiak-.Sostak extension of TML, Fuzzy Sets and Systems 157 (2006), no. 6, 832-842   DOI   ScienceOn
25 Y. Yue and J. Fang, Extension of Shi's quasi-uniformities in a Kubiak-.Sostak sense, Fuzzy Sets and Systems 157 (2006), no. 14, 1956-1969   DOI   ScienceOn