This paper concerns the development of the theory of \(L\)-fuzzy topological spaces in the sense of Hutton and Höhle, where \(L\) denotes a completely distributive lattice. To every \(L\)-fuzzy set in a universe \(X\) a degree (belonging to \(L\)) has been assigned so that contrastedly to Chang's original definition a fuzzy set is no longer open or not but open in some degree. The first contribution treats the decomposition of an \(L\)-fuzzy topology in terms of its \(\alpha\)-level sets and generalizes the earlier work of \textit{P. Wuyts} [Fuzzy Sets Syst. 12, 71--85 (1984; Zbl 0574.54004)]. Secondly, the authors introduce a pointwise ordering between \(L\)-fuzzy topologies on a given universe and they prove some lattice-theoretical properties of some subclasses of the class of \(L\)-topologies. Finally, some characterizations of \(L\)-fuzzy continuous mappings, \(L\)-fuzzy open mappings and \(L\)-fuzzy homeomorphisms between two \(L\)-fuzzy topological spaces (in definition 5.1 the authors forgot the predicate fuzzy) are given.