On fuzzy metrizability

We answer two questions raised by M. A. Erceg [J. Math. Anal. Appl. 69 (1979), 205-230]: precisely we show that the fuzzy unit interval is never T0, except in the standard case, and that a fuzzy pseudo-metrizable T0 space is metrizable in the sense of Erceg (ibid.). Hence the two definitions of metrizable space given in B. Hutton and I. Reilly [Fuzzy Sets and Systems 3 (1980), 93-104] and Erceg (ibid.) are equivalent