Sets In Soft Topological Spaces Research Articles

Soft s∗∗g-Locally Closed Sets

In the present paper, we continue the study of soft semi star generalized closed sets in soft topological spaces by introducing new concepts, namely soft s∗∗g-locally closed sets, soft s∗∗g-locally closed∗ sets, soft s∗∗g-locally closed∗∗ sets.

New generalizations of soft sets in soft topological spaces and their applications

The fundamental objective of the present this article is to display a complete description of novel ideas of generalized soft open and closed sets in soft topological spaces, which are defined as δ-ß-open and δ-ß-closed sets. Various essential properties and characterizations related to these ideas of generalized soft sets have been studied. In addition, the relationship between several well-known ideas of generalized soft open sets such as soft δ-pre-open, soft δ-semi-open, soft pre-open, soft E-open, soft ß-open sets, and soft δ-ß-open sets over the soft topological spaces have been investigated. Furthermore, several appropriate examples to support our main outcomes have been provided.

Soft Generalized αii-Closed Sets in Soft Topological Spaces

This work presented a novel kind of soft generalized closed sets and soft generalized open sets, which we will call soft generalized αii-closed sets and soft generalized αii-open sets in right now paper. The relationships between these two families and several other forms of soft sets, like soft generalized closed, soft generalized ii-closed, soft generalized α-closed, and soft semi-generalized closed sets, are studied and clarified through proofs and evidences such as such as, Theorem8 (If (T,Z) ⊆ (W,Z) ⊆ (X,η,Z) is such that (T,Z) is a sGαICs in (X,η,Z), then (T,Z) is sGαIICs in relation to (W,ηW,Z)), Theorem9 (If (T1,Z),(T2,Z) are sGαIICs, then so is their intersection) and Theorem10 (Each sGαIICs is a sGIICs).

Soft G*β-Separation Axioms in Soft Topological Spaces

Soft set theory is a newly emerging tool to deal with uncertain problems and has been studied by researchers in theory and practice. The concept of soft topological space is a very recently developed area having many research scopes. Soft sets have been studied in proximity spaces, multicriteria decision-making problems, medical problems, mobile cloud computing networks, defense learning system, approximate reasoning etc. In 2020 Punitha Tharani and H. Sujitha introduced a new class of soft generalized star β-closed (Sft*β-closed) sets and Sft*β-open sets in soft topological spaces. They investigated some basic properties of Sft* β-closed sets and Sft*β-open sets. They also studied the relationship between this type of closed sets and other existing closed sets in soft topological spaces. The aim of this paper is to introduce some soft separation axioms called Sftg*β-R0 space, Sftg* β-R1 space, Sftg*β-T0 space, Sftg*β-T1 space, Sftg*β-T2 space, Sftg* β-regular space and Sftg*β-normal space in soft topological spaces. We investigate several properties and characterizations of this spaces in soft topological spaces.

Congruence Representations via Soft Ideals in Soft Topological Spaces

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.

New approach of soft M-open sets in soft topological spaces

The goal of this article is to introduce, investigate and prove several of the properties of M-open and M-closed soft sets in soft topological structure (Sτs). Furthermore, we prove that the collection of soft M-open (SMo) sets is a soft topology by stating and proving the conditions. Finally, we define and study some characteristics of soft M (SM)-continuous function, soft M-irresolute function, soft M-compactness, soft M-connectedness and soft M-separation axioms.

Computing the Cost of Service Projects in Telkaif Town Using Soft Sets and Soft Topology

In this research, we will present a new method of collecting data and performing calculations on it to obtain the required results differently from the usual, at the beginning we will define new concepts of soft sets in soft topological spaces and we will give and explaining many properties of them as soft ii- dense in itself sets, soft ii-connectedness, soft ii-perfection and soft ii-compactness. After that, in the practical part, we will use the concept of soft topology in calculating the cost of service projects in several areas of Telkaif district of Nineveh Governorate in the north of Iraq, whether the cost of projects is in the one area or several areas or all of them using the theory of soft sets in soft topological spaces.

Between the Classes of Soft Open Sets and Soft Omega Open Sets

In this paper, we define the class of soft ω0-open sets. We show that this class forms a soft topology that is strictly between the classes of soft open sets and soft ω-open sets, and we provide some sufficient conditions for the equality of the three classes. In addition, we show that soft closed soft ω-open sets are soft ω0-open sets in soft Lindelof soft topological spaces. Moreover, we study the correspondence between soft ω0-open sets in soft topological spaces and ω0-open sets in topological spaces. Furthermore, we investigate the relationships between the soft α-open sets (respectively, soft regular open sets, soft β-open sets) of a given soft anti-locally countable soft topological space and the soft α-open sets (respectively, soft regular open sets, soft β-open sets) of the soft topological space of soft ω0-open sets generated by it. Finally, we introduce ω0-regularity in topological spaces via ω0-open sets, which is strictly between regularity and ω-regularity, and we also introduce soft ω0-regularity in soft topological spaces via soft ω0-open sets, which is strictly between soft regularity and soft ω-regularity. We investigate relationships regarding ω0-regularity and soft ω0-regularity. Moreover, we study the correspondence between soft ω0-regularity in soft topological spaces and ω0-regularity in topological spaces.

A New Set of Soft Generalized*β-Locally Closed Sets in Soft Topological Spaces

We present a new set of soft generalized* β-locally closed set (here after mentioned as, g ∗ β s -lc), soft g ∗ β − lc ∗set (here after mentioned as, g ∗ β s − lc ∗), soft g ∗ β − lc ∗∗ (here after mentioned as, g ∗ β s − lc ∗∗) sets in STS. Further to the above, the relation between the other notions connected with the forms of soft − lc sets and some properties are studied.

Some Properties of Soft Generalized Open and Closed Sets in Soft Topological Spaces

In this present paper, we introduce and study some soft topological properties of soft ℳ-border, soft ℳ-exterior and soft ℳ-boundary of a soft set using the concept of soft ℳ-open sets and soft ℳ-closed sets and also studied the other property of the well known notion of soft ℳ-interior, ℳ-closure.

Soft Np-Open Sets in Soft Toplogical Spaces

This article is devoted to introduce and study a new kind of soft sets in soft topological spaces called soft Np-open sets as a generalization of soft p-open sets. Also, we investigate and prove some of their properties. By using this new soft set we define and study new soft spaces called soft Np-compact spaces, soft Np-Lindelöf spaces, and obtain some of their characterizations and properties. Finally, we discuss the relationships among soft Np-compact spaces, soft Np-Lindelöf spaces, soft p-compact spaces, soft p-Lindelöf spaces, soft compact spaces, and soft Lindelöf spaces.

Soft Generalized αi-Closed Sets in Soft Topological Spaces

In the present paper, we introduced a new kind of soft generalized closed sets and soft generalized open sets are called soft generalized αi-closed sets and soft generalized αi-open sets. The relations among these two families and some other kinds of soft sets as like as soft generalized closed, soft generalized i-closed, soft generalized α-closed and soft semi-generalized closed sets are investigated and clarify by proofs and evidences.

Regular semiopen soft sets and their applications

The purpose of this paper is to introduce the notion of soft regular semi compactness, connectedness, and separation axioms using regular semiopen soft sets in soft topological spaces. Moreover, we investigate soft RS-regular space and soft RSnormal space are soft to pological properties under bijection, soft regular semi irresolute and soft regular semi irresolute open functions. Also, we show that the properties of being soft regular semi Ti-spaces (i = 1, 2, 3, 4) are hereditary properties.

On soft P_c-connected spaces

In this paper, we define the concept of soft -connected sets and soft -connected spaces by using the notion of soft -open sets in soft topological spaces. Several properties of these concepts are investigated.

Decomposition of soft continuity via soft locally b-closed set

In this paper, we introduce soft locally b-closed sets in soft topological spaces which are defined over an initial universe with a fixed set of parameters and study some of their properties. We investigate their relationships with different types of subsets of soft topological spaces with the help of counterexamples. Also, the concept of soft locally b-continuous functions is presented. Finally, a decomposition of soft continuity is obtained.

On soft pc-separation axioms

AbstractMany mathematicians defined and studied soft separation axioms and soft continuity in soft spaces by using ordinary points of a topological spaceX. Also, some of them studied the same concepts by using soft points. In this paper, we introduce the concepts of soft{p}_{c}-{T}_{i}and soft{p}_{c}-{T}_{i}^{\ast },i=0,1,2by using the concept of soft{p}_{c}-open sets in soft topological spaces. We explore several properties of such spaces. We also investigate the relationship among these spaces and provide a counter example when it is needed.

On Two Classes of Soft Sets in Soft Topological Spaces

In this paper, we define soft ω -open sets and strongly soft ω -open sets as two new classes of soft sets. We study the natural properties of these types of soft sets and we study the validity of the exact versions of some known results in ordinary topological spaces regarding ω -open sets in soft topological spaces. Also, we study the relationships between the ω -open sets of a given indexed family of topological spaces and the soft ω -open sets (resp. strongly soft ω -open sets) of their generated soft topological space. These relationships form a biconditional logical connective which is a symmetry. As an application of strongly soft ω -open sets, we characterize soft Lindelof (resp. soft weakly Lindelof) soft topological spaces.

α -CONNECTEDNESS BETWEEN SOFT SETS

Purpose of the study: In the present paper the concept of soft α -connectedness between soft sets in soft topological spaces has been introduced and studied. The notion of connectedness captures the idea of hanging-togetherness of image elements in an object by given a firmness of connectedness to every feasible path between every possible pair of image elements. It is an important tool for the designing of algorithms for image segmentation. The purpose of this paper is to extend the concept of α –connectedness between sets in soft topology.
 Main Findings: If a soft topological space (X, τ, E) is soft α -connected between a pair of its soft sets, then it is not necessarily that it is soft α -connected between each pair of its soft sets and so it is not necessarily soft α -connected.
 Applications of this study: Image Processing.
 Novelty/Originality of this study: Extend of α -connectedness between soft sets in soft topology.

Soft ξ-open sets in Soft Topological Spaces

The objective of studing the current paper is to introduced a new class of soft open sets in soft topological spaces called soft -open sets. Then soft -open sets are used to study some soft topological concepts. Furthermore, the concept of soft -continuous and almost soft -continuous functions are defined by using the soft -open sets. Some properties and Characterizations of such functions are given.

English

English