Dimension of fuzzy spaces
To define a notion of dimension for fuzzy spaces, the author introduces a new boundary operator which uses subsets of \(X\times (0,1]\). (It could also be described in terms of fuzzy points.) Since his methods can be based on any subset of \(X\times (0,1]\) having non-empty, convex vertical sections, he works with a generalization of fuzzy topological spaces. The resulting inductive dimension is monotone, regular spaces contain subspaces of all smaller dimensions, and zero-dimensional spaces are totally disconnected.
scientific article; zbMATH DE number 4054562