Compactness and weakly induced bifuzzy topological spaces

Safiya, A. S. M. Abu; Fora, Ali; Warner, M. W.

doi:10.1016/0165-0114(94)90075-2

Cited by 3 publications

(3 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then τ j − φ − cl(E) ≤ E, and hence E is fuzzy τ j − φ−cld. Conversely, it is obvious in Theorem 2, also from Figure (1).…”

Section: Types Of Fuzzy Generalized Closed Classes In Fuzzy Bitopolog...mentioning

confidence: 89%

“…Some studies have applied these to the concept of functions that contribute to enriching this research area too [13,18,19]. On the other hand, earlier research on compactness informed our study of this topic [1,21]. A recent study discussed the properties of compactness, but in another field, as G-metric spaces [12] and fuzzy soft space as [22].…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

On Generalized Compactness in Fuzzy Bitopological Spaces

Ahmed Alharbi,

Kilicman

2024

Eur. J. Pure Appl. Math.

View full text Add to dashboard Cite

The main objective of this research is to study some types of generalized closed sets in fuzzy bitopology including $(i,j)-g\alpha-cld$, $(i,j)-gs-cld$, $(i,j)-gp-cld$, and $(i,j)-g\beta-cld$. We then present basic theorems for determining their relationships and explain their properties, such as closure and interior. In addition, there are many interesting counterexamples. The last part of the research focuses on generalized compactness in fuzzy bitopological spaces and their types and explores the relationships between these concepts, their important theories, and some relevant counterexamples. The results established in this paper are new in the domain of fuzzy bitopology.

show abstract

“…Then τ j − φ − cl(E) ≤ E, and hence E is fuzzy τ j − φ−cld. Conversely, it is obvious in Theorem 2, also from Figure (1).…”

Section: Types Of Fuzzy Generalized Closed Classes In Fuzzy Bitopolog...mentioning

confidence: 89%

Section: Introductionmentioning

confidence: 98%

On Generalized Compactness in Fuzzy Bitopological Spaces

Ahmed Alharbi,

Kilicman

2024

Eur. J. Pure Appl. Math.

View full text Add to dashboard Cite

show abstract

“…There is a voluminous literature for BiTop concerning separation, compactness, connectedness, completion, connections to uniform and quasi-uniform spaces, homotopy groups and algebraic topology, relationships to bilocales [2], a recently emerging role in programming semantics [25], etc. A significant part of the recent literature on bitopology is in lattice-valued mathematics [30,27,50,51]. Letting L be a us-quantale (Subsection 1.2 below) and X a set, the triple (X, τ, σ) is an L-bitopological space if τ, σ are L-topologies on X (Subsection 1.5); and such spaces with L-bicontinuous mappings comprise the category L-BiTop.…”

mentioning

confidence: 99%

Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics

Rodabaugh

2008

Appl.Gen.Topol.

View full text Add to dashboard Cite

Abstract. This paper studies various functors between (latticevalued) topology and (lattice-valued) bitopology, including the ex-2 -Top introduced in this paper, both of which are extremely well-behaved strict, concrete, full embeddings. Given the greater simplicity of lattice-valued topology vis-a-vis latticevalued bitopology and the fact that the class of L 2 -Top's is strictly smaller than the class of L-Top's encompassing fixed-basis topology, the class of E×'s makes the case that lattice-valued bitopology is categorically redundant. As a special application, traditional bitopology as represented by BiTop is (isomorphic in an extremely well-behaved way to) a strict subcategory of 4-Top, where 4 is the four element Boolean algebra; this makes the case that traditional bitopology is a special case of a much simpler fixed-basis topology.

show abstract

On compactness in bifuzzy topological spaces

Srivastava

2001

Fuzzy Sets and Systems

View full text Add to dashboard Cite

Compactness and weakly induced bifuzzy topological spaces

Cited by 3 publications

References 8 publications

On Generalized Compactness in Fuzzy Bitopological Spaces

On Generalized Compactness in Fuzzy Bitopological Spaces

Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics

On compactness in bifuzzy topological spaces

Contact Info

Product

Resources

About