On fuzzy metrizability

Abstract

In this paper 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 T 0 except in the standard case and that a fuzzy pseudo-metrizable T 0 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.