Completions of uniform convergence spaces

1971 ◽  
Vol 194 (2) ◽  
pp. 83-108 ◽  
Author(s):  
Ellen E. Reed
Keyword(s):  
Uniform Convergence ◽  
Convergence Spaces

scholarly journals Order compatibility for Cauchy spaces and convergence spaces

1987 ◽  
Vol 10 (2) ◽  
pp. 209-216
Author(s):  
D. C. Kent ◽  
Reino Vainio
Keyword(s):  
Uniform Convergence ◽  
Weak Order ◽  
Convergence Spaces ◽  
Convergence Structure ◽  
Cauchy Structure ◽  
Cauchy Spaces

A Cauchy structure and a preorder on the same set are said to be compatible if both arise from the same quasi-uniform convergence structure onX. Howover, there are two natural ways to derive the former structures from the latter, leading to “strong” and “weak” notions of order compatibility for Cauchy spaces. These in turn lead to characterizations of strong and weak order compatibility for convergence spaces.

On the Regularity of the Kowalsky Completion

1984 ◽  
Vol 36 (1) ◽  
pp. 58-70 ◽  
Author(s):  
Eva Lowen-Colebunders
Keyword(s):  
Uniform Convergence ◽  
Essential Role ◽  
Convergence Spaces ◽  
The Past ◽  
Cauchy Space ◽  
Cauchy Spaces

Cauchy spaces were introduced by Kowalsky in 1954 [9]. In that paper a first completion method for these spaces was given. In 1968 Keller [5] has shown that the Cauchy space axioms characterize the collections of Cauchy filters of uniform convergence spaces in the sense of [1]. Moreover in the completion theory of uniform convergence spaces the associated Cauchy structures play an essential role [12]. This fact explains why in the past ten years in the theory of Cauchy spaces, much attention has been given to the study of completions.

scholarly journals The category of uniform convergence spaces is cartesian closed

1976 ◽  
Vol 15 (3) ◽  
pp. 461-465 ◽  
Author(s):  
R.S. Lee
Keyword(s):  
Uniform Convergence ◽  
Function Spaces ◽  
Convergence Spaces ◽  
Cartesian Closedness ◽  
Cartesian Closed ◽  
And Function

This paper first assigns specific uniform convergence structures to the products and function spaces of pairs of uniform convergence spaces, and then establishes a bijection between corresponding sets of morphisms which yields cartesian closedness.

scholarly journals Coarse uniform convergence spaces

1975 ◽  
Vol 61 (1) ◽  
pp. 143-150
Author(s):  
R. J. Gazik ◽  
Darrell Kent
Keyword(s):  
Uniform Convergence ◽  
Convergence Spaces

StratifiedL-uniform convergence spaces

2005 ◽  
Vol 28 (1) ◽  
pp. 11-36 ◽  
Author(s):  
G. Jäger ◽  
M.H. Burton
Keyword(s):  
Uniform Convergence ◽  
Convergence Spaces
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