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\(m^{*}\)-fuzzy basically disconnected spaces in smooth fuzzy topological spaces. (English) Zbl 1274.54021

Summary: In this paper, the concepts of \(m^{*} r\)-fuzzy \(\tilde {g}\)-open \(F_{\sigma }\) sets and \(m^{*}\)-fuzzy basically disconnected spaces are introduced in the sense of Šostak and Ramadan. Some interesting properties and characterizations are studied. The Tietze extension theorem for \(m^{*}\)-fuzzy basically disconnected spaces is discussed.

MSC:

54A40 Fuzzy topology
03E72 Theory of fuzzy sets, etc.