A new approach for fuzzy topology. II (Q1193648)

This paper is a continuation of [the author, ibid. 39, 303-321 (1991; Zbl 0718.54017)] where the concept of a fuzzifying topology is introduced. (A fuzzifying topology on a set \(X\) is a mapping \({\mathcal T}: 2^ X\to I\) satisfying ``natural'' axioms.) Here the author considers the notions of interior, boundary, connectedness, and axioms of countability in the context of fuzzifying topologies. It is important to emphasize that all these concepts are defined by means of fuzzy predicates, i.e. are essentially fuzzy, as different from the properties of the same name considered in the traditional (i.e. Chang-Goguen's) approach to fuzzy topology. Besides, the operation of taking subspaces in the category of fuzzifying topological spaces is studied in the paper.