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Separation axioms, subspaces and sums in fuzzy topology. (English) Zbl 0543.54006

Separation axioms are extended to fuzzy topological spaces. The authors define \(FT_ 0\), \(FT_ 1\), \(FT_ s\), \(FT_ 2\), \(FT_ 3\) and \(FT_ 4\) spaces, and, by means of counterexamples, they point out the non- coincidence of the different notions of separation. The remarkable deviation from ordinary topology is found in the non-productivity of the regularity property; localized separation axioms are also introduced in fuzzy setting. The authors also study the hereditary and the additivity behaviour of \(C_ I\), \(C_{II}\), separability and some types of compactness in fuzzy setting.
Reviewer: S.Ganguly

MSC:

54A40 Fuzzy topology
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54D30 Compactness
54B10 Product spaces in general topology
54B35 Spectra in general topology
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References:

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