^{}Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen- zhen, P.R. China

Abstract

In this paper, it is shown that the category of $L$-ordered fuzzifying convergence spaces contains the category of pretopological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory and the latter contains the category of topological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory. Also, it is proved that the category of $L$-ordered fuzzifying convergence spaces can be embedded in the category of stratified $L$-ordered convergence spaces as a coreflective subcategory.

[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, Wiley, New York, 1990. [2] J. M. Fang, Stratied L-ordered convergence structures, Fuzzy Sets Syst., 161 (2010), 2130{ 2149. [3] J. M. Fang, Relationships between L-ordered convergence structures and strong L-topologies, Fuzzy Sets Syst., 161(22) (2010), 2923{2944. [4] J. Gutierrez Garca, I. Mardones Perez and M. H. Burton, The relationship between various lter notions on a GL-Monoid, J. Math. Anal. Appl., 230(1999), 291{302. [5] U. Hohle and A. P. Sostak, Axiomatic foudations of xed-basis fuzzy topology, in: U. Hohle, 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. [6] U. Hohle, Characterization of L-topologies by L-valued neighborhoods, Chapter 5, In [5], 389{432. [7] U. Hohle, Many valued topology and its applications, Kluwer Academic Publishers, Boston, Dordrecht, London, 2001. [8] G. Jager, A category of L-fuzzy convergence spaces, Quaest. Math., 24 (2001), 501{517. [9] G. Jager, Subcategories of lattice-valued convergence spaces, Fuzzy Sets Syst., 156 (2005), 1{24. [10] G. Jager, Pretopological and topological lattice-valued convergence spaces, Fuzzy Sets Syst., 158 (2007), 424{435. [11] B. Y. Lee, J. H. Park and B. H. Park, Fuzzy convergence structures, Fuzzy Sets Syst., 56 (1993), 309{315. [12] L. Q. Li and Q. Jin, On stratied L-convergence spaces: Pretopological axioms and diagonal axioms, Fuzzy Sets Syst., 204 (2012), 40{52. [13] E. Lowen, R. Lowen and P. Wuyts, The categorical topological approach to fuzzy topology and fuzzy convergence, Fuzzy Sets Syst., 40 (1991), 347{373. [14] K. C. Min, Fuzzy limit spaces, Fuzzy Sets Syst., 32 (1989), 343{357.

[15] B. Pang and J. M. Fang, L-fuzzy Q-convergence structures, Fuzzy Sets Syst., 182 (2011), 53{65. [16] B. Pang, On (L;M)-fuzzy convergence spaces, Fuzzy Sets Syst., 238 (2014), 46{70. [17] B. Pang, Enriched (L;M)-fuzzy convergence spaces, J. Intell. Fuzzy Syst., 27(1) (2014), 93{103. [18] B. Pang and F. G. Shi Degrees of compactness of (L;M)-fuzzy convergence spaces and its applications, J. Intell. Fuzzy Syst., 251 (2014), 1{22. [19] W. C. Wu and J. M. Fang, L-ordered fuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 9(2) (2012), 147{161. [20] L. S. Xu, Characterizations of fuzzifying topologies by some limit structures, Fuzzy Sets Syst., 123 (2001), 169{176. [21] W. Yao, On many-valued stratied L-fuzzy convergence spaces, Fuzzy Sets Syst., 159 (2008), 2503{2519. [22] W. Yao, On L-fuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 6(1) (2009), 63{80.