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In [25], Katsaras introduced a method for constructing a Hutton [0, 1]-quasi-uniformity from a crisp uniformity. In this paper we present other different methods for making this based mainly in the concept of a fuzzy uniform structure. Furthermore, we prove that some of these methods preserve the completeness property of the quasi-uniformity. Moreover, we also show that Katsaras’ construction allows to develop a theory of completion of a Hutton [0,1]-quasi-uniform space obtained from a uniform space. [ABSTRACT FROM AUTHOR]

Abstract: A well-known result on Moscow spaces states that every -dense subset of a Moscow space X is C-embedded in X. We present here the selection version of this result and also (by means of two different approaches) we use selection theory to characterize the open bounded subsets of a uniform space in the case when its completion is a Moscow space. [Copyright &y& Elsevier]

This paper is devoted to study a special kind of extensions of dynamical systems which are introduced by considering completions of totally bounded uniform spaces. It is proved that transitivity, minimality and chaos (in Devaney''s sense) are carried over these class of extensions. [Copyright &y& Elsevier]

Abstract: In the spirit of the well-known constructions of Edalat and Heckmann for metric spaces, we endow the set of formal (closed) balls of a given uniform space with a structure of poset and prove several of its properties, which extend to the uniform framework the corresponding ones of metric spaces. In particular, to show under what conditions this poset is a dcpo we introduce and discuss a weak notion of uniform completeness. Some illustrative examples are also given. [Copyright &y& Elsevier]

Abstract: This paper deals with fuzzy uniform structures previously introduced by the authors [Fuzzy uniform structures and continuous t-norms, Fuzzy Sets Syst. 161 (2009) 1011–1021]. Our approach involves a covariant functor from the category of fuzzy uniform spaces and fuzzy uniformly continuous mappings (in our sense) to the category of uniform spaces and uniformly continuous mappings. We show that is well-behaved with respect to some significant fuzzy uniform concepts, and its behavior provides a method to introduce notions of fine fuzzy uniform structure and Stone–Čech fuzzy compactification in this context. Our method also applies to obtain fuzzy versions of some classical results on topological algebra and hyperspaces. The case of quasi-uniform structures is also analyzed. [Copyright &y& Elsevier]

Abstract: 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 mappings) by means of a covariant functor. Moreover, we also describe the inverse functor and, then, we discuss completeness and completion of these fuzzy uniform structures. It follows from our results that each fuzzy uniform structure in our sense induces a Hutton [0, 1]-uniformity and, conversely, each Hutton [0, 1]-uniformity induces a fuzzy uniform structure in our sense. [Copyright &y& Elsevier]