Abstract: This paper deals with $[0,1]$-Hutton (quasi)-uniform spaces. Completeness of a Hutton $[0,1]$-uniform space is investigated. The main result states the equivalence between completeness of any fuzzy-(quasi)-metric space $(X, M, \ast)$ and completeness of the induced $[0,1]$-Hutton quasi-uniform space $(X,{\mathfrak{U}}_{M})$. Also it is proved that a $[0,1]$-Hutton (quasi)-uniform space induced by a fuzzy-(quasi)-metric space has a bicompletion unique up to quasi-uniform isomorphisms. The obtained results come from an appropriate definition of Cauchy $L$-filter (where $L$ stands for a complete lattice, with additional properties).

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