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Regularity in fuzzy convergence spaces. (English) Zbl 0992.54009

The authors’ abstract: “The notions of regularity and weak regularity are introduced in the category of fuzzy convergence spaces, and each is shown to be an extension of regularity with respect to the embedding functor from the category of convergence spaces. Moreover, the category whose objects are weakly regular fuzzy spaces is topological and thus initial and final regular structures exist. The relationship between regularity and a diagonal condition is given.

MSC:

54A40 Fuzzy topology
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54B30 Categorical methods in general topology
18B30 Categories of topological spaces and continuous mappings (MSC2010)
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