Fuzzy filters
Let X be a set and I the unit interval. In fuzzy topology, subsets of X (which can be identified with mappings from X to \(\{\) 0,1\(\})\) are replaced by so-called fuzzy sets (which by definition, are mappings from X to I). In the same spirit, topological concepts defined in terms of the lattice structure on \({\mathfrak P}(X)\) (ordered by \(A\subset B)\) are replaced by their fuzzy counterparts defined in terms of the lattice structure on \({\mathcal F}(X;I)\) (ordered by \(A\leq B)\). The authors introduce fuzzy filters, explain their convergence and characterize fuzzy topological concepts (such as open sets, closed sets, adherent points and continuity) by means of filter convergence.
scientific article; zbMATH DE number 4056525