The general fuzzy filter approach to fuzzy topology. II
By means of the notion of fuzzy filter developed in Part I [ibid. 205-224 (1995; Zbl 0873.54008), see the review above], here the author characterizes fuzzy topologies by interior operators, fuzzy neighborhoods, fuzzy neighborhood filters, fuzzy neighborhood operators, open fuzzy filters, interior fuzzy filter operators \(\dots\) (the fuzzy topologies can be identified with the monadic topologies with respect to the partially ordered fuzzy filter monad). Further notions for fuzzy filters treated here are trace, inner and adherence point, projective openness and closeness, closure operator, compactness; usual properties of subsets, continuous functions and products are shown to be valid. Previous results on stratified fuzzy topologies (all constant fuzzy sets are open) are included in a natural manner as special cases.
scientific article; zbMATH DE number 919471