A new approach for fuzzy topology. II. (English) Zbl 0752.54002

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.
Reviewer: A.Šostak (Riga)


54A40 Fuzzy topology
03B52 Fuzzy logic; logic of vagueness
03B50 Many-valued logic


Zbl 0718.54017
Full Text: DOI


[1] Kelley, J. L., General Topology (1955), Van Nostrand: Van Nostrand New York · Zbl 0066.16604
[2] Ying, M. S., A new approach for fuzzy topology (I), Fuzzy Sets and Systems, 39, 303-321 (1991) · Zbl 0718.54017
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