Some Classes of Soft Functions Defined by Soft Open Sets Modulo Soft Sets of the First Category

Ameen, Zanyar A.; Alqahtani, Mesfer H.

doi:10.3390/math11204368

Cited by 9 publications

(4 citation statements)

References 37 publications

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“…The conclusions in this article are preliminary, and more study will be necessary. These findings can be seen as the foundation for researching new topics of soft topology (see [40]). Also, the obtained results are essential for the growth of soft measure theory.…”

Section: Discussionmentioning

confidence: 80%

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Congruence Representations via Soft Ideals in Soft Topological Spaces

Ameen,

Alqahtani

2023

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This article starts with a study of the congruence of soft sets modulo soft ideals. Different types of soft ideals in soft topological spaces are used to introduce new weak classes of soft open sets. Namely, soft open sets modulo soft nowhere dense sets and soft open sets modulo soft sets of the first category. The basic properties and representations of these classes are established. The class of soft open sets modulo the soft nowhere dense sets forms a soft algebra. Elements in this soft algebra are primarily the soft sets whose soft boundaries are soft nowhere dense sets. The class of soft open sets modulo soft sets of the first category, known as soft sets of the Baire property, is a soft σ-algebra. In this work, we mainly focus on the soft σ-algebra of soft sets with the Baire property. We show that soft sets with the Baire property can be represented in terms of various natural classes of soft sets in soft topological spaces. In addition, we see that the soft σ-algebra of soft sets with the Baire property includes the soft Borel σ-algebra. We further show that soft sets with the Baire property in a certain soft topology are equal to soft Borel sets in the cluster soft topology formed by the original one.

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Section: Discussionmentioning

confidence: 80%

“…This mission is completed by the diagram at the end of this work, which displays the relationships between the previously mentioned soft sets. We encourage that the reader compare Figure 1 here with Figure 1 in [40].…”

Section: Conflicts Of Interestmentioning

confidence: 97%

Congruence Representations via Soft Ideals in Soft Topological Spaces

Ameen,

Alqahtani

2023

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“…In 2011, Ahmad and Kharal [9] applied the continuity notions to soft set theory [10,11]. Several classes of generalized soft open sets and soft functions defined in [12][13][14]. Zorlutuna [15] investigated more interesting properties of soft continuity.…”

Section: Introductionmentioning

confidence: 99%

Strictly Wider Class of Soft Sets via Supra Soft δ-Closure Operator

Abd El-latif,

Alqahtani,

Gharib

2024

Int. J. Anal. Appl.

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In this work, we use the supra soft δ-closure operator to present a new notion of generalized closed sets in supra soft topological spaces (or SSTSs), named supra soft δ-generalized closed sets. We show that, this notion is more general than many of previous notions, which presented before in famous papers. We illustrate many of its essential properties in detail. Specifically, we illustrate that the new collection neither forms soft topology nor supra soft topology. Moreover, we study the behavior of the soft image and soft pre-images of supra soft δ-generalized closed sets under new types of soft mappings, named supra soft irresolute and supra soft δ-irresolute closed. In addition, we define the concept of supra soft δ-generalized open sets, as a complement of supra soft δ-generalized closed sets. Finally, the relationships with other forms of generalized open sets in SSTSs are explored, supported by concrete examples and counterexamples. Therefore, I think the development of the notions presented in this paper are sufficiently general relevance to allow for future extensions.

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“…In recent years, many authors have contributed to soft set theory in the different fields such as topology, algebra, see e.g. [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

On R-fuzzy Soft δ-Open Sets and Applications via Fuzzy Soft Topologies

Alshammari,

Alqahtani,

Taha

2024

Preprint

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In this paper, we first define the concepts of r-fuzzy soft α-open (semi-open and δ-open) sets on fuzzy soft topological spaces based on the article Aygunoglu et al. (Hacet. J. Math. Stat., 43 (2014), 193-208), and the relations of these sets with each other are established. In addition, we introduce the concepts of fuzzy soft δ-closure (δ-interior) operators, and study some properties of them. Also, the concept of r-fuzzy soft δ-connected sets is introduced and studied with help of fuzzy soft δ-closure operators. Thereafter, we define the concepts of fuzzy soft α-continuous (β-continuous, semi-continuous, pre-continuous and δ-continuous) functions, which are weaker forms of fuzzy soft continuity, and some properties of these functions along with their mutual relationships are discussed. Moreover, a decomposition of fuzzy soft α-continuity and a decomposition of fuzzy soft semi-continuity is obtained. Finally, as a weaker form of a fuzzy soft continuity, the concepts of fuzzy soft almost (weakly) continuous functions are defined, and some properties are specified. Additionally, we explore the notion of continuity in a very general setting called, fuzzy soft (L, M, N, O)-continuous functions and a historical justification is introduced.

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Some Classes of Soft Functions Defined by Soft Open Sets Modulo Soft Sets of the First Category

Cited by 9 publications

References 37 publications

Congruence Representations via Soft Ideals in Soft Topological Spaces

Congruence Representations via Soft Ideals in Soft Topological Spaces

Strictly Wider Class of Soft Sets via Supra Soft δ-Closure Operator

On R-fuzzy Soft δ-Open Sets and Applications via Fuzzy Soft Topologies

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