Categorical structures of soft groups

Öztunç, Simge; Aslan, Sedat; Dutta, Hemen

doi:10.1007/s00500-020-05362-0

Cited by 15 publications

(6 citation statements)

References 14 publications

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“…Goldar et al [25] gave a new definition of soft rings and soft ideals using soft elements. Öztunç et al [26] constructed the category of soft groups and soft group homomorphisms. Anjum et al [27] discussed two different types of soft hemirings, soft intersection and soft union.…”

Section: Introductionmentioning

confidence: 99%

Bijective soft rings with applications

Koyuncu

2024

Journal of New Results in Science

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In recent years, soft sets have been widely used in many important decision-making real-life problems. In this paper, observing the usage of soft sets in such kind of vital problems, we have introduced the bijective-unitary bijective soft rings. Firstly, we have defined and exemplified a bijective soft ring and a unitary bijective soft ring. Moreover, we have presented some applications of bijective soft rings. We have shown the usage of bijective soft rings in coding theory. In this context, we have observed that by obtaining a bijective soft ring over a finite ring, we have a coding matrix to encode a given set of messages. Besides these applicable results, we have also obtained some relations between bijective soft and classical rings.

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Section: Introductionmentioning

confidence: 99%

Bijective soft rings with applications

Koyuncu

2024

Journal of New Results in Science

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“…In 2011, the concept of soft topology was defined by Shabir and Naz [4]. Many classical TS concepts were then incorporated into STSs in [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and other works.…”

Section: Introductionmentioning

confidence: 99%

On Soft Generalized ω-Closed Sets and Soft T1/2 Spaces in Soft Topological Spaces

Ghour

2022

Axioms

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In this paper, we define a soft generalized ω-closed set, which is a generalization of both the soft ω-closed set and the soft generalized closed set. We show that the classes of generalized closed sets and generalized ω-closed sets coincide in soft anti-locally countable soft topological spaces. Additionally, in soft locally countable soft topological spaces, we show that every soft set is a soft generalized ω-closed set. Furthermore, we prove that the classes of soft generalized closed sets and soft generalized ω-closed sets coincide in the soft topological space (X,τω,A). In addition to these, we determine the behavior of soft generalized ω-closed sets relative to soft unions, soft intersections, soft subspaces, and generated soft topologies. Furthermore, we investigate soft images and soft inverse images of soft generalized closed sets and soft generalized ω-closed sets under soft continuous, soft closed soft transformations. Finally, we continue the study of soft T1/2 spaces, in which we obtain two characterizations of these soft spaces, and investigate their behavior with respect to soft subspaces, soft transformations, and generated soft topologies.

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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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Categorical structures of soft groups

Cited by 15 publications

References 14 publications

Bijective soft rings with applications

Bijective soft rings with applications

On Soft Generalized ω-Closed Sets and Soft T1/2 Spaces in Soft Topological Spaces

Weaker Forms of Soft Regular and Soft T2 Soft Topological Spaces

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