On fuzzification of topological categories

This paper shows that (L,M)-fuzzy topology of U. Höhle, T. Kubiak and A. Šostak is an instance of a general fuzzification procedure for topological categories, which amounts to the construction of a new topological category from a given one. This fuzzification procedure motivates a partial dualization of the machinery of tower extension of topological constructs of D. Zhang, thereby providing the procedure of tower extension of topological categories. With the help of this dualization, we arrive at the meta-mathematical result that the concept of (L,M)-fuzzy topology and the notion of approach space of R. Lowen are “dual” to each other.