Completions of uniform convergence spaces

1971 ◽  
Vol 194 (2) ◽  
pp. 83-108 ◽  
Author(s):  
Ellen E. Reed
1987 ◽  
Vol 10 (2) ◽  
pp. 209-216
Author(s):  
D. C. Kent ◽  
Reino Vainio

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.


1984 ◽  
Vol 36 (1) ◽  
pp. 58-70 ◽  
Author(s):  
Eva Lowen-Colebunders

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.


1976 ◽  
Vol 15 (3) ◽  
pp. 461-465 ◽  
Author(s):  
R.S. Lee

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.


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

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

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