The Topological Modification of the L-fuzzy Unit Interval

Abstract

In 1975, Hutton invented the L-fuzzy unit interval I(L) a very fruitful concept which enabled him to characterize the normal L-fuzzy topological spaces in terms of Urysohn’s type lemma and to introduce a very efficient complete regularity axiom for L-fuzzy spaces (see [Hutton 1975 1977]). Although the appropriateness of I(L) as a space which plays the same role in fuzzy topology as the real unit interval plays in general topology, has been proved by a number of other authors (e.g. [Liu 1983], [Liu and Luo 1989], [Rodabaugh 1983b, 1988a], [Kubiak 1987, 1986]), the structure of this canonical L-fuzzy space is not yet well-understood. A survey of the results on the L-fuzzy unit interval that have been obtained up to 1982 was made by [Rodabaugh 1982a]. That paper, however, contains more open questions than results.