The stratified canonical fuzzy topology on \(I(I)\) is uniformizable
Let \(L\) be a completely distributive lattice with an order reversing involution, \(I(L)\) an \(L\)-fuzzy unit interval. \textit{S. E. Rodabaugh} posed a question whether or not the stratified canonical fuzzy topology on \(I(L)\) is uniformizable [see J. Math. Anal. Appl. 129, 37-70 (1988; Zbl 0637.54007)]. The author gives a positive answer for the case \(L=I\). Moreover, he has also proved the uniformity obtained has a countable base, therefore, the corresponding topology on \(I(I)\) is metrizable. The author claims that his proof depends on the property of the real \(I\) and the argument holds only for the case \(L=I\). But, the recent work of the author [Fuzzy Sets Syst. 54, 225-227 (1993)] shows that for general case, there is still a positive answer to Rodabaugh's question.
scientific article; zbMATH DE number 150640