On initial and final fuzzy uniform structures
The paper is devoted to the study of initial and final structures in the category FUN of fuzzy uniform spaces introduced in [\textit{W. Gähle}, \textit{F. Bayoumi}, \textit{A. Kandil} and \textit{A. Nouh}, ibid. 97, 225-254 (1998; Zbl 0934.54004)]. The existence of initial and final lifts (and hence the existence of initial and final structures) in the category FUN is proved. By means of special initial structures subspaces and products in FUN are characterized. It is shown that the fuzzy topology \({\mathcal T}_{{\mathcal U}}\) generated by the fuzzy uniform structure \({\mathcal U}\), which is initial for a family of fuzzy uniform structures \(\{{\mathcal U}_i, i\in{\mathcal I}\}\), is initial for the family of corresponding generated fuzzy topologies \(\{{\mathcal T}_{{\mathcal U}_i}, i\in{\mathcal I}\}\).
scientific article; zbMATH DE number 1868237