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.
On fuzzy metrizability
ARTICO, GIULIANO;MORESCO, ROBERTO
1985
Abstract
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.File in questo prodotto:
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