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

1974 ◽  
pp. 172-187 ◽  
Author(s):  
Anthony W. Hager
Keyword(s):  
Continuous Functions ◽  
Uniform Spaces ◽  
Vector Lattices ◽  
Categorical Methods ◽  
Uniformly Continuous

Categorical characterization of uniform hyperspaces

1983 ◽  
Vol 94 (2) ◽  
pp. 229-233 ◽  
Author(s):  
J. M. Harvey
Keyword(s):  
Uniform Spaces ◽  
Categorical Methods ◽  
Continuous Maps ◽  
Uniformly Continuous

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.

Regular completions of uniform convergence spaces

1974 ◽  
Vol 11 (3) ◽  
pp. 413-424 ◽  
Author(s):  
R.J. Gazik ◽  
D.C. Kent ◽  
G.D. Richardson
Keyword(s):  
Uniform Convergence ◽  
Real Line ◽  
Dual Space ◽  
Function Algebra ◽  
Continuous Functions ◽  
Convergence Space ◽  
Uniform Spaces ◽  
Convergence Spaces ◽  
Uniform Convergence Space ◽  
Uniformly Continuous

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.

scholarly journals On vector lattices and rings of uniformly continuous functions

1966 ◽  
Vol 6 (1) ◽  
pp. 23-29
Author(s):  
L. Aparina
Keyword(s):  
Continuous Functions ◽  
Vector Lattices ◽  
Uniformly Continuous

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

Uniform Continuity of Continuous Functions on Uniform Spaces

1961 ◽  
Vol 13 ◽  
pp. 657-663 ◽  
Author(s):  
Masahiko Atsuji
Keyword(s):  
Real Function ◽  
Metric Spaces ◽  
Uniform Space ◽  
Continuous Functions ◽  
Uniform Continuity ◽  
Uniform Structure ◽  
Uniform Spaces ◽  
Continuous Real Function ◽  
Complete Space ◽  
Uniformly Continuous

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.

LIFTING THE FUNCTOR ITO THE CATEGORY OF UNIFORM SPACES

2020 ◽  
Vol 4 (1) ◽  
pp. 29-39
Author(s):  
Dilrabo Eshkobilova ◽  
Keyword(s):  
Compact Support ◽  
Probability Measures ◽  
Uniform Spaces ◽  
Continuous Maps ◽  
Uniformly Continuous

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

scholarly journals A study of uniformities on the space of uniformly continuous mappings

2020 ◽  
Vol 18 (1) ◽  
pp. 1478-1490
Author(s):  
Ankit Gupta ◽  
Abdulkareem Saleh Hamarsheh ◽  
Ratna Dev Sarma ◽  
Reny George
Keyword(s):  
Uniform Space ◽  
Uniform Spaces ◽  
Continuous Mappings ◽  
Uniformly Continuous

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.

scholarly journals Lattices of uniformly continuous functions

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

scholarly journals Regular vector lattices of continuous functions and Korovkin-type theorems–-Part II

2006 ◽  
Vol 172 (1) ◽  
pp. 69-90 ◽  
Author(s):  
Francesco Altomare ◽  
Mirella Cappelletti Montano
Keyword(s):  
Continuous Functions ◽  
Vector Lattices ◽  
Korovkin Type Theorems
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