On \(Q\)-sobriety. (English) Zbl 1421.54005
Summary: The study of fixed-basis variety-based topology was initiated by S. A. Solovyov in [Fuzzy Sets Syst. 159, No. 19, 2567–2585 (2008; Zbl 1177.54004)], which, among other things, generalizes fuzzy topology. We extend within this framework, an earlier result due to A. K. Srivastava and A. S. Khastgir [Inf. Sci. 110, No. 3–4, 195–205 (1998; Zbl 0930.54012)], which showed that the category of sober fuzzy topological spaces is the epireflective hull of the fuzzy Sierpinski space in the category of \(T_0\)-fuzzy topological spaces.
MSC:
| 54A40 | Fuzzy topology |
| 18B30 | Categories of topological spaces and continuous mappings (MSC2010) |
Keywords:
\(\Omega\)-algebra; \(Q\)-topological space; \(Q\)-sober topological space; \(Q\)-\(T_0\)-topological space; epireflective hullReferences:
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