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We prove that given a fuzzy metric space (in the sense of Kramosil and Michalek), the completion of its Hausdorff fuzzy metric space is isometric to the Hausdorff fuzzy metric space of its completion, when the Hausdorff fuzzy metrics are defined on the respective collections of non-empty closed subsets. As a consequence, we deduce the corresponding result… (More)

Stone-Weierstrass-type theorems for groups of group-valued functions with discrete range or discrete domain are obtained. We study criteria for a subgroup of the group of continuous functions C(X, G) (X compact, G a topological group) to be uniformly dense. These criteria are based on the existence of so-called condensing functions, where a continuous… (More)

We introduce and discuss a notion of fuzzy uniform structure that provides a direct link with the classical theory of uniform spaces. More exactly, for each continuous t-norm we prove that the category of all fuzzy uniform spaces in our sense (and fuzzy uniformly continuous mappings) is isomorphic to the category of uniform spaces (and uniformly continuous… (More)

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