Local T_3 Constant Filter Convergence Spaces

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.

A note on separation and compactness in categories of convergence spaces

Applied General Topology ◽

10.4995/agt.2003.2005 ◽

2003 ◽

Vol 4 (1) ◽

pp. 1 ◽

Cited By ~ 1

Author(s):

Mehmet Baran ◽

Muammer Kula

Keyword(s):

Topological Category ◽

Convergence Spaces ◽

Filter Convergence

In previous papers, various notions of compact, T3, T4, 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.

Cartesian-closedness and subcategories of (L, M)-fuzzy Q-convergence spaces

Soft Computing ◽

10.1007/s00500-021-06057-w ◽

2021 ◽

Author(s):

Bin Pang ◽

Lin Zhang

Keyword(s):

Convergence Spaces ◽

Cartesian Closedness

Epis in categories of convergence spaces

Acta Mathematica Hungarica ◽

10.1007/bf01874680 ◽

1993 ◽

Vol 61 (3-4) ◽

pp. 195-201 ◽

Cited By ~ 5

Author(s):

D. Dikranjan ◽

E. Giuli

Keyword(s):

Convergence Spaces

An adaptive filter convergence method for echo cancellation and decision feedback equalization

10.1109/icassp.1986.1168853 ◽

2005 ◽

Cited By ~ 4

Author(s):

A. Kanemasa ◽

A. Sugiyama

Keyword(s):

Adaptive Filter ◽

Decision Feedback ◽

Echo Cancellation ◽

Decision Feedback Equalization ◽

Filter Convergence ◽

Convergence Method

Asymmetric filter convergence and completeness

Quaestiones Mathematicae ◽

10.2989/16073606.2013.779972 ◽

2013 ◽

Vol 36 (2) ◽

pp. 291-308

Author(s):

John Frith ◽

Anneliese Schauerte

Keyword(s):

Filter Convergence

Order compatibility for Cauchy spaces and convergence spaces

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171287000279 ◽

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 sequentially regular convergence spaces

Czechoslovak Mathematical Journal ◽

10.21136/cmj.1967.100772 ◽

1967 ◽

Vol 17 (2) ◽

pp. 232-247

Author(s):

Václav Koutník

Keyword(s):

Regular Convergence ◽

Convergence Spaces ◽

Sequentially Regular

Convergence Classes of L -Filters in L , M -Fuzzy Topological Spaces

Journal of Mathematics ◽

10.1155/2021/8246173 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Ting Yang ◽

Sheng-Gang Li ◽

William Zhu ◽

Xiao-Fei Yang ◽

Ahmed Mostafa Khalil

Keyword(s):

Topological Spaces ◽

Convergence Spaces ◽

Topological Convergence ◽

Convergence Structure ◽

Fuzzy Topological Spaces ◽

The Relationship

An L , M -fuzzy topological convergence structure on a set X is a mapping which defines a degree in M for any L -filter (of crisp degree) on X to be convergent to a molecule in L X . By means of L , M -fuzzy topological neighborhood operators, we show that the category of L , M -fuzzy topological convergence spaces is isomorphic to the category of L , M -fuzzy topological spaces. Moreover, two characterizations of L -topological spaces are presented and the relationship with other convergence spaces is concretely constructed.