Compactification of lattice-valued convergence spaces

Jäger, Gunther

doi:10.1016/j.fss.2009.10.010

Cited by 12 publications

(5 citation statements)

References 8 publications

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“…• As a further application of ⊺-ultrafilters, we can define compactness of a ⊺-convergence space. Motivated by the compactification of stratified L-generalized convergence spaces [12], we will also consider the compactification of ⊺-convergence spaces.…”

Section: Discussionmentioning

confidence: 99%

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Subcategories of the category of $\top$-convergence spaces

Gao

Pang

2024

Hacettepe Journal of Mathematics and Statistics

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T-convergence structures serve as an important tool to describe fuzzy topology and deserve more and more attention. This paper aims to give further investigations onT-convergence structures. Firstly, several types of $\top$-convergence structures are introduced, including Kent T-convergence structures, T-limit structures and principal T-convergence structures, and their mutual categorical relationships as well as their own categorical properties are studied. Secondly, by changing of the underlying lattice, the ``change of base" approach is applied to T-convergence structures and the relationships between T-convergence structures with respect to different underlying lattices are demonstrated.

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Section: Discussionmentioning

confidence: 99%

“…Pang [20] proposed (L, M )-fuzzy convergence structures by means of (L, M )-fuzzy filters. Many scholars paid attention to these kinds of fuzzy convergence structures from different aspects (see, e.g., Jäger [12][13][14][15], Fang [3,4], Li et al [17][18][19], Pang [21][22][23] and Zhang [32,34]).…”

Section: Introductionmentioning

confidence: 99%

Subcategories of the category of $\top$-convergence spaces

Gao

Pang

2024

Hacettepe Journal of Mathematics and Statistics

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“…Since ϕ : X −→ X, x → exe is continuous, it follows from [26] that eXe is compact subset of X, and by Lemma 3.5 [27], eXe is -closed; as H(e) ⊆ eXe, we have U ( eXe ) = , therefore, y ∈ eXe. Also, note that lim F U(e) = .…”

Section: Complete Heyting Algebra-valued Convergencementioning

confidence: 97%

“…Then A is compact if and only if for every stratified H-ultrafilter U ∈ F su H (X) with U( A ) = there is an x ∈ A such that lim U(x) = Lemma 2.10. ( [26,27]) Let (X, lim) and Y, lim be stratified H-generalized convergence spaces, and f : (X, lim) −→ Y, lim be continuous. If A ⊆ X is compact, then f (A) is a compact subset of Y, lim .…”

Section: Definition 24 ([19]mentioning

confidence: 99%

Complete Heyting algebra-valued convergence semigroups

Ahsanullah

Al-Thukair

2018

Filomat

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Considering a complete Heyting algebra H, we introduce a notion of stratified H-convergence semigroup. We develop some basic facts on the subject, besides obtaining conditions under which a stratified H-convergence semigroup is a stratified H-convergence group. We supply a variety of natural examples; and show that every stratified H-convergence semigroup with identity is a stratified H-quasiuniform convergence space. We also show that given a commutative cancellative semigroup equipped with a stratified H-quasi-unifom structure satisfying a certain property gives rise to a stratified H-convergence semigroup via a stratified H-quasi-uniform convergence structure.

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“…other different approaches to Stone-Čech type fuzzy compactifications see, for instance, [12,18]). Fuzzy uniform structures on topological groups and hyperspaces are studied in Section 4 and Section 5, respectively.…”

Section: Introductionmentioning

confidence: 99%

Standard fuzzy uniform structures based on continuous t-norms

García

Romaguera

Sanchis

2012

Fuzzy Sets and Systems

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Compactification of lattice-valued convergence spaces

Cited by 12 publications

References 8 publications

Subcategories of the category of $\top$-convergence spaces

Subcategories of the category of $\top$-convergence spaces

Complete Heyting algebra-valued convergence semigroups

Standard fuzzy uniform structures based on continuous t-norms

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