On the reflectivity and coreflectivity of \(L\)-fuzzyfying topological spaces in \(L\)-topological spaces.
Considering \(L\) as a completely distributive lattice, the author proves that the well-known category TOP of topological spaces can be embedded in the category \(L\)-FYS of \(L\)-fuzzifying topological spaces as a both bireflective and bicoreflective full subcategory, although TOP contains no simultaneously bireflective and bicoreflective full subcategories [\textit{V. Kannan}, Math. Ann. 195, 168--174 (1972; Zbl 0215.09701)]. The author also proves that the category \(L\)-FYS can be embedded in the category \(L\)-TOP of stratified Chang-Gougen topological spaces as a simultaneously bireflective and bicoreflective full subcategory. Various relationships among some other categories are also investigated.
scientific article; zbMATH DE number 1757446