Regular convergence spaces

1967 ◽  
Vol 174 (1) ◽  
pp. 1-7 ◽  
Author(s):  
C. H. Cook ◽  
H. R. Fischer
Keyword(s):  
Regular Convergence ◽  
Convergence Spaces

r-Regular Convergence Spaces

1944 ◽  
Vol 66 (1) ◽  
pp. 69 ◽  
Author(s):  
Paul A. White
Keyword(s):  
Regular Convergence ◽  
Convergence Spaces

P-Regular Convergence Spaces

1990 ◽  
Vol 149 (1) ◽  
pp. 215-222 ◽  
Author(s):  
D. C. Kent ◽  
G. D. Richardson
Keyword(s):  
Regular Convergence ◽  
Convergence Spaces

scholarly journals p-topological andp-regular: dual notions in convergence theory

1999 ◽  
Vol 22 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Scott A. Wilde ◽  
D. C. Kent
Keyword(s):  
Natural Duality ◽  
Convergence Theory ◽  
Convergence Criteria ◽  
Convergence Space ◽  
Regular Convergence ◽  
Convergence Spaces ◽  
Simple Characterization ◽  
Topological Convergence

The natural duality between “topological” and “regular,” both considered as convergence space properties, extends naturally top-regular convergence spaces, resulting in the new concept of ap-topological convergence space. Taking advantage of this duality, the behavior ofp-topological andp-regular convergence spaces is explored, with particular emphasis on the former, since they have not been previously studied. Their study leads to the new notion of a neighborhood operator for filters, which in turn leads to an especially simple characterization of a topology in terms of convergence criteria. Applications include the topological and regularity series of a convergence space.

scholarly journals REGULAR CONVERGENCE SPACES

2013 ◽  
Vol 21 (4) ◽  
pp. 375-382
Author(s):  
Jin Won Park
Keyword(s):  
Regular Convergence ◽  
Convergence Spaces

Epis in categories of convergence spaces

1993 ◽  
Vol 61 (3-4) ◽  
pp. 195-201 ◽  
Author(s):  
D. Dikranjan ◽  
E. Giuli
Keyword(s):  
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.

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