Soft ξ-open sets in Soft Topological Spaces

2017

The main objective of this paper is to introduce and define a new class of sets called soft -open sets in soft topological spaces, which is subclass of soft pre-open sets. Several properties of this kind of sets are obtained. By using this soft set we present and study the concept of soft -continuous functions.

Abstract and Applied Analysis, 2014

We introduce softα-sets on soft topological spaces and study some of their properties. We also investigate the concepts of softα-continuous and softα-open functions and discuss their relationships with soft continuous and other weaker forms of soft continuous functions. Also counterexamples are given to show the noncoincidence of these functions.Corrigendum to “Soft α-Open Sets and Soft α-Continuous Functions”

Iraqi Journal of Science, 2020

In this paper, we offer and study a novel type generalized soft-open sets in topological spaces, named soft Ƅc-open sets. Relationships of this set with other types of generalized soft-open sets are discussed, definitions of soft Ƅ , soft bc- closure and soft bc- interior are introduced, and its properties are investigated. Also, we introduce and explore several characterizations and properties of this type of sets.

Journal of new theory, 2017

this paper, a new class of generalized soft open sets in soft topological spaces, called soft e-open set is focused and investigated some properties of them. Then focused the relationships among soft δ-pre open sets, soft δ-semi open sets, soft pre-open sets and soft e-open sets. We also investigated the concepts of soft e-open functions, soft e-continuous, soft e-irresolute and soft e-homeomorphism on soft topological space and discussed their relations with existing soft continuous and other weaker forms of soft continuous functions. Further soft e-separation axioms have been introduced and investigated with the help of soft e-open sets. Finally, we observed that the collection Ser-h(X,τ,E) form a soft group.

Kyungpook mathematical journal, 2014

This paper introduces semiopen and semiclosed soft sets in soft topological spaces. The notions of interior and closure are generalized using these sets. A detail study is carried out on properties of semiopen, semiclosed soft sets, semi interior and semi closure of a soft set in a soft topological space. Various forms of soft functions, like semicontinuous, irresolute, semiopen soft functions are introduced and characterized. Further soft semicompactness, soft semiconnectedness and soft semiseparation axioms are introduced and studied.

2021

In this paper, we define a soft somewhat open set using the soft interior operator. We study main properties the class of soft somewhat open sets that is contained in the class soft somewhere dense sets. Then, we introduce the classes of soft somewhat continuous and soft somewhat open functions and soft somewhat homeomorphisms. Moreover, we study properties and characterizations of soft somewhat continuous and soft somewhat open functions. At last, we discuss topological invariants for soft somewhat homeomorphisms. Multiple examples are offered to clarify some invalid results.

Wasit journal for pure sciences, 2024

In the context of soft classes, Athar Kharal and B. Ahmad [6] defined a soft mapping and investigated some characteristics of soft set images and inverse images. The references ([7], [8] [9], [10], [11], [12], [13]) introduced and ABSTRACT: This paper introduces novel concepts of soft functions known as soft-irresolute, soft-open, and soft-closed function as well as some of their properties. The interrelationships of this newly defined soft functions with other types of soft functions are investigated, and the behaviors of soft-irresolute (respectively, soft-open, and soft-closed) functions under soft composition are studied. Finally, using soft-open sets, the concepts of soft-Hausdorff space are introduced and investigated.

Afrika Matematika, 2017

In this paper, we introduce soft locally b-closed sets in soft topological spaces which are de…ned over an initial universe with a …xed set of parameters and study some of their properties. We investigate their relationships with di¤erent 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.

Journal of Universal Mathematics

The aim of this paper is to produce new decompositions of soft continuity. For this reason, we first have introduced two new sets concepts named as soft AC-set with soft BC-set in soft topological spaces. Compairing with this two soft sets concepts and others soft set kinds, we have obtained two decompositions of soft open sets, supported by counterexamples. Utilizing soft AC-set and soft BC-set concepts, we have introduced two functions concepts named as soft AC-continuous with soft BC-continuous functions and we have obtained a new decomposition of soft continuity.

Mathematics

Soft topological spaces (STSs) have received a lot of attention recently, and numerous soft topological ideas have been created from differing viewpoints. Herein, we put forth a new class of generalizations of soft open sets called “weakly soft semi-open subsets” following an approach inspired by the components of a soft set. This approach opens the door to reformulating the existing soft topological concepts and examining their behaviors. First, we deliberate the main structural properties of this class and detect its relationships with the previous generalizations with the assistance of suitable counterexamples. In addition, we probe some features that are obtained under some specific stipulations and elucidate the properties of the forgoing generalizations that are missing in this class. Next, we initiate the interior and closure operators with respect to the classes of weakly soft semi-open and weakly soft semi-closed subsets and look at some of their fundamental characteristics...