scholarly journals A note on separation and compactness in categories of convergence spaces

2003 ◽  
Vol 4 (1) ◽  
pp. 1 ◽  
Author(s):  
Mehmet Baran ◽  
Muammer Kula
Keyword(s):  
Topological Category ◽  
Convergence Spaces ◽  
Filter Convergence

<p>In previous papers, various notions of compact, T<sub>3</sub>, T<sub>4</sub>, and Tychonoff objects in a topological category were introduced and compared. The main objective of this paper is to characterize each of these classes of objects in the categories of filter and local filter convergence spaces as well as to examine how these various generalizations are related.</p>

scholarly journals Probabilistic convergence spaces

1996 ◽  
Vol 61 (3) ◽  
pp. 400-420 ◽  
Author(s):  
G. D. Richardson ◽  
D. C. Kent
Keyword(s):  
Basic Theory ◽  
Convergence In Probability ◽  
Previous Theory ◽  
Convergence Spaces ◽  
Convergence Almost Everywhere ◽  
Almost Everywhere ◽  
Filter Convergence

AbstractA basic theory for probabilistic convergence spaces based on filter convergence is introduced. As in Florescu's previous theory of probabilistic convergence structures based on nets, one is able to assign a probability that a given filter converges to a given point. Various concepts and theorems pertaining to convergence spaces are extended to the realm of probabilistic convergence spaces, and illustrated by means of examples based on convergence in probability and convergence almost everywhere. Diagonal axioms due to Kowalsky and Fischer are also studied, first for convergence spaces and then in the setting of probabilistic convergence spaces.

scholarly journals T0 and T1 semiuniform convergence spaces

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 537-546 ◽  
Author(s):  
Mehmet Baran ◽  
Sumeyye Kula ◽  
Ayhan Erciyes
Keyword(s):  
Uniform Convergence ◽  
Topological Category ◽  
Convergence Spaces

In previous papers, various notions of T0 and T1 objects in a topological category were introduced and compared. In this paper, we characterize each of these classes of objects in categories of various types of uniform convergence spaces and compare them with the usual ones as well as examine how these generalizations are related.

scholarly journals Local T_3 Constant Filter Convergence Spaces

2020 ◽  
Vol 33 (2) ◽  
pp. 446-454
Author(s):  
Ayhan ERCİYES ◽  
Tesnim Meryem BARAN
Keyword(s):  
Convergence Spaces ◽  
Filter Convergence

Epis in categories of convergence spaces

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

Asymmetric filter convergence and completeness

2013 ◽  
Vol 36 (2) ◽  
pp. 291-308
Author(s):  
John Frith ◽  
Anneliese Schauerte
Keyword(s):  
Filter Convergence

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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