In this paper, we give a kind of Cauchy 1-completeness in probabilistic quasi-uniform spaces by using 1-filters. Utilizingthe relationships among probabilistic quasi-uniformities, classical quasi-uniformities and Hutton [0, 1]-quasi-uniformities,we show the relationships between their completeness. In fuzzy quasi-metric spaces, we establish the relationshipsbetween the completeness of induced p...

The aim of this paper is to study induced (quasi-)uniformities in Kramosil and Michalek's fuzzy metric spaces. Firstly, $I$-uniformity in the sense of J. Guti'{e}rrez  Garc'{i}a and $I$-neighborhood system in the sense of H"{o}hle and u{S}ostak are induced by the given fuzzy metric. It is shown that the fuzzy metric and the induced $I$-uniformity will generate the same $I$-neighborhood system. ...

In cite{Kats84}, Katsaras introduced a method for constructing a Hu-tton $[0,1]$-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' con...

The aim of this paper is to present a fuzzy counterpart method of constructing the Hausdorff quasi-uniformity of a crisp quasi-uniformity. This process, based on previous works due to Morsi cite{Morsi94} and Georgescu cite{Georgescu08}, allows to extend probabilistic and Hutton $[0,1]$-quasi-uniformities on a set $X$ to its power set.  In this way, we obtain an endofunctor for each one of the c...

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 func...

and Applied Analysis 3 The quasi-uniform space X,U will always be considered to be a topological space with the topology obtained by using as the family of all neighborhoods of a point x0 ∈ X all sets of the formU x0 {x ∈ X : x0, x ∈ U}, whereU runs overU. Such a topology is called topology of the quasi-uniformity. Note that each topology onX is induced by a quasi-uniformity see 8, 9 , the most...

Publications Methodological articles [1] J L Hutton. Non-negative time series models for dry river flow. [2] J L Hutton and R G Owens. Bayesian sample size calculations and prior beliefs about child sexual abuse. [5] J L Hutton and P J Solomon. Parameter orthogonality in mixed regression models for survival data. Individual patient data meta-analysis of randomised anti-epileptic drug monotherap...

For any weightable quasi-metric space (X, d) having a maximum with respect to the associated order ≤d, the notion of the quasi-metric of complexity convergence on the the function space (equivalently, the space of sequences) X, is introduced and studied.We observe that its induced quasi-uniformity is finer than the quasi-uniformity of pointwise convergence and weaker than the quasi-uniformity o...