On \(R_ 0\) and \(R_ 1\) fuzzy topological spaces: A counterexample (Q803990)

\textit{A. K. Srivastava} introduced in this journal 127, 151-157 (1987; Zbl 0621.54004)] a notion of \(R_ 1\)-ness for fuzzy topological spaces, and claims in Theorem 3 that his property is initial. However, both the theorem and the proof are incorrect. The theorem is true for finite families but as will follow from the example given here, an infinite product of \(R_ 1\)-spaces need not even be \(R_ 0\). Also the counterexample 3.4 in the joint paper with \textit{R. Srivastava} and \textit{S. N. Lal}, ibid. 136, No.1, 66-73 (1988; see the preceding review) is incorrect.