# Categories of two types of uniform spaces

• Kim Yong-Chan (Department of Mathematics, Kangnung National University) ;
• Lee Seok-Jong (Department of Mathematics, Chungbuk National University)
• Published : 2006.09.01

#### Abstract

In a strictly two-sided, commutative biquantale, we study the relationships between the categories of Hutton (L, $\bigotimes$)- uniform spaces and (L, $\bigodot$ )-uniform spaces. We investigate the properties of them.

#### References

1. J. Gutierrez Garia, M. A. de Prade Vicente and A.P. Sostak, 'A unified approach to the concept of fuzzy L-uniform spaces,' Chapter 3 in [12], 81-114
2. U. Hohle, Many valued topology and its applications, Kluwer Academic Publisher, Boston, 2001
3. U. Hohle and E. P. Klement, Non-classical logic and their applications to fuzzy subsets, Kluwer Academic Publisher, Boston, 1995
4. U. Hohle and S. E. Rodabaugh, 'Mathematics of Fuzzy Sets, Logic, Topology and Measure Theory,' The Handbooks of Fuzzy Sets Series, Volume 3, Kluwer Academic Publishers, Dordrecht (1999)
5. B. Hutton, 'Uniformities on fuzzy topological spaces,' J. Math. Anal. Appl. 58 (1977), 559-571 https://doi.org/10.1016/0022-247X(77)90192-5
6. A. K. Katsaras, 'Fuzzy quasi-proximities and fuzzy quasi-uniformities,' Fuzzy Sets and Systems 27(1988), 335-343 https://doi.org/10.1016/0165-0114(88)90059-0
7. Y. C. Kim and Y. S. Kim, 'Two types of uniform spaces,' International Jouranl of Fuzzy Logic and Intelligent Systems 6 (2006), no. 1, 77-84 https://doi.org/10.5391/IJFIS.2006.6.1.077
8. Y. C. Kim and J. M. Ko, 'The images and preim-ages of L-filterbases,' (Article in press) Fuzzy Sets and Systems
9. W. Kotze, 'Uniform spaces,' Chapter 8 in [4], 553-580
10. Kubiak, Mardones-Perez and Prada-Vicente, 'Luniform spaces versus I (L)-uniform spaces,' (Article in press) Fuzzy Sets and Systems
11. R. Lowen, 'Fuzzy uniform spaces,' J. Math. Anal. Appl. 82(1981), 370-385 https://doi.org/10.1016/0022-247X(81)90202-X
12. S. E. Rodabaugh, E. P. Klement, 'Toplogical And Algebraic Structures In Fuzzy Sets,' The Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic 20, Kluwer Academic Publishers, (Boston/Dordrecht/London) (2003)
13. S. E. Rodabaugh, 'Axiomatic foundations for uniform operator quasi-uniformities,' Chapter 7 in [12] 199-233