Soft Topological Transformation Groups

Oğuz, Gülay

doi:10.3390/math8091545

Cited by 10 publications

(8 citation statements)

References 21 publications

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“…Then, the collection ℬ consisting of all sets = {  * ( ) ∶ ⊆ ,  } is a base for the topology * on * ( ) denoted by * . [10] Let ( , +, •) be a hyperring and ( , ) be a topological space. In this case, algebraic hyperstructure ( , +, •, ) is said to be a topological hyperring if three hyperoperations ' + ', ' • ' and '/' are continuous.…”

Section: • =mentioning

confidence: 99%

“…Successful results have been obtained using the soft set theory to solve complex problems in many fields such as economics, engineering, social sciences, medical science and others. Indeed, this theory has been applied with different perspectives in diverse areas such as algebra, topology, analysis and geometry by many mathematicians [10,11,12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

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Idealistic Soft Topological Hyperrings

Oğuz

2020

Sci Inquiry Rev.

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The aim of this article is to introduce the concept of an idealistic soft topological hyperring over a hyperring. Some structural properties of this concept are also studied. Moreover, this study investigates the relationship between the idealistic soft topological hyperrings and the idealistic soft hyperrings. Finally, the restricted (extended) intersection and ∧-intersection of the family of the idealistic soft topological hyperrings are examined.

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Section: • =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Idealistic Soft Topological Hyperrings

Oğuz

2020

Sci Inquiry Rev.

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“…The family of all soft closed sets in (X, τ, A) will be denoted by τ c . Soft topological concepts and their applications are still a hot area of research ( [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]). The notion of ω-regular TSs was introduced in [23], then the study of ω-regular TSs continued in [24] in which the authors defined and investigated ω-T 2 TSs.…”

Section: Introductionmentioning

confidence: 99%

Weaker Forms of Soft Regular and Soft T2 Soft Topological Spaces

Ghour

2021

Mathematics

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Soft ω-local indiscreetness as a weaker form of both soft local countability and soft local indiscreetness is introduced. Then soft ω-regularity as a weaker form of both soft regularity and soft ω-local indiscreetness is defined and investigated. Additionally, soft ω-T2 as a new soft topological property that lies strictly between soft T2 and soft T1 is defined and investigated. It is proved that soft anti-local countability is a sufficient condition for equivalence between soft ω-locally indiscreetness (resp. soft ω-regularity) and soft locally indiscreetness (resp. soft ω-regularity). Additionally, it is proved that the induced topological spaces of a soft ω-locally indiscrete (resp. soft ω-regular, soft ω-T2) soft topological space are (resp. ω-regular, ω-T2) topological spaces. Additionally, it is proved that the generated soft topological space of a family of ω-locally indiscrete (resp. ω-regular, ω-T2) topological spaces is soft ω-locally indiscrete and vice versa. In addition to these, soft product theorems regarding soft ω-regular and soft ω-T2 soft topological spaces are obtained. Moreover, it is proved that soft ω-regular and soft ω-T2 are hereditarily under soft subspaces.

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“…Recently, in [12], the author introduced the notion of soft topological polygroups by applying soft set theory to topological polygroups. In addition, see [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

On Soft Topological Polygroups and Their Examples

Mousarezaei

Davvaz

2021

IJFIS

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Polygroups are a special subclass of hypergroups that satisfies group-like axioms. A polygroup is a multigroup that is completely regular and reversible in itself. A topological polygroup is a polygroup P with a topology on P that satisfies certain conditions. Moreover, the concept of soft sets is a general mathematical tool for dealing with uncertainty. In this study, we investigate soft topological polygroups over a polygroup. The ideas presented in this article can be used to build more polygroups and soft topological polygroups.

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Soft Topological Transformation Groups

Cited by 10 publications

References 21 publications

Idealistic Soft Topological Hyperrings

Idealistic Soft Topological Hyperrings

Weaker Forms of Soft Regular and Soft T2 Soft Topological Spaces

On Soft Topological Polygroups and Their Examples

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