Vector lattices of uniformly continuous functions and some categorical methods in uniform spaces

Author(s):  
Anthony W. Hager
1983 ◽  
Vol 94 (2) ◽  
pp. 229-233 ◽  
Author(s):  
J. M. Harvey

In this paper, we use categorical methods to arrive at a characterization of Hausdorff hyperspaces of separated uniform spaces within a category of ordered uniform spaces. We begin by showing that the hyperspace construction gives rise to a monad H in the category Uni of non-empty separated uniform spaces and uniformly continuous maps. We then identify the category of H-algebras and characterize hyperspaces in this context.


1974 ◽  
Vol 11 (3) ◽  
pp. 413-424 ◽  
Author(s):  
R.J. Gazik ◽  
D.C. Kent ◽  
G.D. Richardson

A regular completion with universal property is obtained for each member of the class of u–embedded uniform convergence spaces, a class which includes the Hausdorff uniform spaces. This completion is obtained by embedding each u-embedded uniform convergence space (X, I) into the dual space of a complete function algebra composed of the uniformly continuous functions from (X, I) into the real line.


1966 ◽  
Vol 6 (1) ◽  
pp. 23-29
Author(s):  
L. Aparina

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Л. В. Апарина. О векторных решетках и кольцах равномерно непрерывных функций L. Aparina. Apie tolygiai tolydinių funkcijų vektorines gardeles ir žiedus


1961 ◽  
Vol 13 ◽  
pp. 657-663 ◽  
Author(s):  
Masahiko Atsuji

Recently several topologists have called attention to the uniform structures (in most cases, the coarsest ones) under which every continuous real function is uniformly continuous (let us call the structures the [coarsest] uc-structures), and some important results have been found which closely relate, explicitly or implicitly, to the uc-structures, such as in the vS of Hewitt (3) and in the e-complete space of Shirota (7). Under these circumstances it will be natural to pose, as Hitotumatu did (4), the problem: which are the uniform spaces with the uc-structures? In (1 ; 2), we characterized the metric spaces with such structures, and in this paper we shall give a solution to the problem in uniform spaces (§ 1), together with some of its applications to normal uniform spaces and to the products of metric spaces (§ 2). It is evident that every continuous real function on a uniform space is uniformly continuous if and only if the uniform structure of the space is finer than the uniform structure defined by all continuous real functions on the space.


2020 ◽  
Vol 4 (1) ◽  
pp. 29-39
Author(s):  
Dilrabo Eshkobilova ◽  

Uniform properties of the functor Iof idempotent probability measures with compact support are studied. It is proved that this functor can be lifted to the category Unif of uniform spaces and uniformly continuous maps


2020 ◽  
Vol 18 (1) ◽  
pp. 1478-1490
Author(s):  
Ankit Gupta ◽  
Abdulkareem Saleh Hamarsheh ◽  
Ratna Dev Sarma ◽  
Reny George

Abstract New families of uniformities are introduced on UC(X,Y) , the class of uniformly continuous mappings between X and Y, where (X,{\mathcal{U}}) and (Y,{\mathcal{V}}) are uniform spaces. Admissibility and splittingness are introduced and investigated for such uniformities. Net theory is developed to provide characterizations of admissibility and splittingness of these spaces. It is shown that the point-entourage uniform space is splitting while the entourage-entourage uniform space is admissible.


2013 ◽  
Vol 160 (1) ◽  
pp. 50-55 ◽  
Author(s):  
Félix Cabello Sánchez ◽  
Javier Cabello Sánchez

2006 ◽  
Vol 172 (1) ◽  
pp. 69-90 ◽  
Author(s):  
Francesco Altomare ◽  
Mirella Cappelletti Montano

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