Abstract
It is shown that the category of non‐Archimedean metric spaces with 1‐Lipschitz maps can be embedded as a coreflective non‐bireflective subcategory in the category of fuzzy uniform spaces. Consequential characterizations of topological and uniform properties are derived.
Highlights
We show that the category NA(1) of non-Archimedean metric spaces with metric bounded by and with morphisms the non-expanslve maps is coreflectively embedded in the category FUS of fuzzy uniform spaces [4], [9] in an extremely simple and natural way
We recall [i0], [Ii] that a uniformity U on X is called non-Archimedean if there exists a collection @ of partitions of X such that U p pip e } is a basis for U
Summary
We show that the category NA(1) of non-Archimedean metric spaces with metric bounded by and with morphisms the non-expanslve maps is coreflectively embedded in the category FUS of fuzzy uniform spaces [4], [9] in an extremely simple and natural way. Through the forgetful functor FUS FNS [5] each space in NA(1) determines a non-topologically generated space in FNS, the topological modification (i.e. TOP-coreflection) of which is nothing else the metric topology. If d .< is a non-Archimedean pseudometric on a set X, {}, with := 1- d, is a basis for a fuzzy uniformity ](d) on X, where. If U is a fuzzy uniformity on X, having a singleton basis {}, this function satisfies the conditions a, b, c in Lemma 3.1.2 and U ](d) where d:= 1-@ is a non-Archimedean pseudometric.
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