On extended fuzzy topologies
This is one of four papers in which the authors develop a theory of extended fuzzy topologies based on fuzzy stacks [J. Fuzzy Math. 6, No. 1, 223-261 (1998; Zbl 0909.54003); ibid., No. 3, 539-574 (1998; Zbl 0913.54007); 575-608 (1998; Zbl 0913.54008)]. Here they present basic results on preimages of fuzzy stacks and fuzzy stack products, on extended fuzzy topologies (characterized by fuzzy neighbourhood stacks and by fuzzy neighbourhoods) and on initial and final extended fuzzy topologies (subspace, product, quotient, sum). The category of extended fuzzy topological spaces is shown to be a complete, cocomplete, topological category and important bireflective and bicoreflective subcategories are studied.
strongly stratified extended fuzzy topology
scientific article; zbMATH DE number 1400259