Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces

Document Type: Research Paper

Author

School of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China

Abstract

The definition of $L$-fuzzy Q-convergence spaces is presented by Pang and Fang in 2011. However, Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces is not investigated. This paper focuses on Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces, and it is shown that  the category $L$-$\mathbf{QFCS}$ of $L$-fuzzy Q-convergence spaces is Cartesian-closed.

Keywords


[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete category, Wiley, New York,
1990.
[2] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182{190.
[3] J. M. Fang, Categories isomorphic to L-FTOP, Fuzzy Sets Syst., 157 (2006), 820{831.
[4] H. R. Fischer, Limeraume, Math. Ann., 137 (1959), 269{303.
[5] U. Hohle and A. P. Sostak, Axiomatic foundations of xed-basis fuzzy topology, in: U.Hohle,
S.E.Rodabaugh(Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, in:
Handbook Series, vol.3, Kluwer Academic Publishers, Dordrecht, (1999), 123{173.
[6] U. Hohle, Probabilistic metrization of fuzzy uniformities, Fuzzy Sets Syst., 8 (1982), 63{69.
[7] G. Jager, A category of L-fuzzy convergence spaces, Quest. Math., 24 (2001), 501{517.
[8] T. Kubiak, On fuzzy topologies, Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, 1985.
[9] Y. M. Liu and M. K. Luo, Fuzzy topology, World Scienti c Publication, Singapore, 1998.
[10] B. Pang and J. M. Fang, L-fuzzy Q-convergence structures, Fuzzy Sets Syst., 182 (2011),
53{65.
[11] B. Pang, Further study on L-fuzzy Q-convergence structures, Iranian Journal of Fuzzy Systems,
10(5) (2013), 147{164.
[12] B. Pang, On (L;M)-fuzzy convergence spaces, Fuzzy Sets Syst., 238 (2014), 46{70.
[13] B. Pang, Enriched (L;M)-fuzzy convergence spaces , J. Intell. Fuzzy Syst., 27 (2014), 93{103.
[14] B. Pang and F. G. Shi, Degree of compactness of (L;M)-fuzzy convergence spaces and its
applications, Fuzzy Sets Syst., 251 (2014), 1{22.
[15] G. Preuss, Foundations of Topology{An Approach to Convenient Topology, Kluwer Academic
Publisher, Dordrecht, Boston, London, 2002.
[16] A. P. Sostak, On a fuzzy topological structure, Rend. Circ. Mat. Palermo (Suppl. Ser. II), 11
(1985), 89{103.
[17] W. Yao, On L-fuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 6(1) (2009),
63{80.
[18] W. Yao, On many-valued strati ed L-fuzzy convergence spaces, Fuzzy Sets Syst., 159 (2008),
2503{2519.
[19] M. S. Ying, A new approach to fuzzy topology (I), Fuzzy Sets Syst., 39 (1991), 303{321.