Petrićević, Zlata \(R_ 0\) and \(R_ 1\) axioms in fuzzy topology. (English) Zbl 0693.54004 Mat. Vesn. 41, No. 1, 21-28 (1989). We introduce and study \(R_ 0\) and \(R_ 1\) axioms for fuzzy topological spaces \((FR_ 0\) and \(FR_ 1\), for short), which are in a natural way analogous to that of \(R_ 0\) and \(R_ 1\) axioms in general topology and present several characterizations of \(FR_ 0\) and \(FR_ 1\) axioms and study some of its basic properties, like its preservation under topological product and topological sum etc. Implications between the different axioms are studied. In the last section we give a definition of properly compact fuzzy set and prove a theorem: An \(FR_ 1\) space is \(FT_ 2\) space iff every properly compact fuzzy set is closed. MSC: 54A40 Fuzzy topology 54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.) PDFBibTeX XMLCite \textit{Z. Petrićević}, Mat. Vesn. 41, No. 1, 21--28 (1989; Zbl 0693.54004)