On modular approximants in sequential convergence 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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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

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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.

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On $\frak B$-convergence spaces

Czechoslovak Mathematical Journal ◽

10.21136/cmj.1968.100856 ◽

1968 ◽

Vol 18 (4) ◽

pp. 569-588

Author(s):

Karel Wichterle

Keyword(s):

Convergence Spaces

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