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2021, Filomat
The aim of the article is to point out a one-to-one correspondence between soft topological spaces over a universe U with respect to a parameter set E and topological ones on the Cartesian product E x U. From this point of view, all soft topological terms, soft operations, soft functions and properties of soft topological spaces are actually topological concepts. Because the set valued mappings and set valued analysis have great application potential, it is necessary to look for their meaningful use with respect to standard topological methods and set valued analysis procedures.
Journal of Applied Mathematics, Statistics and Informatics, 2020
In this paper, we have established topological soft sets over generalized topological spaces and topological spaces, and studied its structural properties. We have derived a topological soft set in any given topological space, and from this point of view, we have given necessary and sufficient condition for homeomorphic Alexandroff spaces using topological soft set technique. At last, we have derived a topological soft set using closed sets in any topological space and we have given necessary and sufficient condition for arbitrary homeomorphic topological spaces using them.
Mathematical Sciences and Applications E-Notes, 2020
In this paper, using the concept of soft topology given in [9] i.e. with our new perspective of soft topology, we give some basic topological concepts such as open soft set, closed soft set, interior and closure of a soft set. We then give the concept of soft continuity of a given function between soft topological spaces, and from here we also define the concept of soft homeomorphism and argue the all obtained results. At the end of the article, we propose a decision-making method using soft topological concepts.
Hacettepe Journal of Mathematics and Statistics, 2016
The paper deals with a soft topological space which is defined over an initial universe set U with a fixed set of parameters E. The main goal is to point out that any soft topological space is homeomorphic to a topological space (E × U, τ) where τ is an arbitrary topology on the product E × U , consequently many soft topological notions and results can be derived from general topology. Furthermore, in many papers some notions are introduced by different ways and it would be good to give a unified approach for a transfer of topological notions to a soft set theory and to create a bridge between general topology and soft set theory.
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.
Science journal of University of Zakho, 2019
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.
Hittite Journal of Science & Engineering, 2018
A lmost every branch of science has its own uncertainties and ambiguities. These uncertainties depend on the existence of many parameters. So it is not always easy to model a daily life problem mathematically using classical mathematical methods. In this sense, mankind has gone to find new mathematical models. In 1999, Molodtsov [1] established the soft set theory to model uncertainties in any phenomenon. He defined the concept of soft set as follows; Definition 1.1. Set-theoretic operations for soft sets given by Maji et al. and Ali et al. in [2, 3]. The operations between two soft sets such as soft union, soft intersection, soft complement etc. defined in [2, 3] as follows.
Computers & Mathematics with Applications, 2011
The concept of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this work, we define the soft topology on a soft set, and present its related properties. We then present the foundations of the theory of soft topological spaces.
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.
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”
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.
Computers & Mathematics with Applications, 2011
In the present paper we introduce soft topological spaces which are defined over an initial universe with a fixed set of parameters. The notions of soft open sets, soft closed sets, soft closure, soft interior points, soft neighborhood of a point and soft separation axioms are introduced and their basic properties are investigated. It is shown that a soft topological space gives a parametrized family of topological spaces. Furthermore, with the help of an example it is established that the converse does not hold. The soft subspaces of a soft topological space are defined and inherent concepts as well as the characterization of soft open and soft closed sets in soft subspaces are investigated. Finally, soft T i-spaces and notions of soft normal and soft regular spaces are discussed in detail. A sufficient condition for a soft topological space to be a soft T 1-space is also presented.
Mathematical Methods in the Applied Sciences, 2020
In this article, we give some new properties of elementary operations on soft sets and then we introduce a new soft topology by using elementary operations over a universal set with a set of parameters called elementary soft topology. Also, we define a topology, members of which are collections of the soft elements and give the relation between this topology and elementary soft topology. We show that this new soft topology is different from those previously defined soft topologies. We prove some of the properties of the topological concepts we investigate in this topology. Finally, we describe soft function and soft continuity and give an application of the soft function as soft set approach to the rotation in E 3 .
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.
Soft Computing, 2021
The paper points out the methodological aspects of soft topological spaces which are defined over an initial universe set U with a fixed set of parameters E. The basic change of view is due to the fact that soft topology is actually a topology on the product of two sets, and in many cases, standard methods of general topology can be applied. Furthermore, in many papers some notions are introduced by different ways and it would be good to give a unified approach for a transfer of topological notions to a soft set theory and to create a bridge between general topology and soft set theory. On the other hand, not all counterparts of soft concepts are studied on classical topology and some types of separation axioms support this fact.
The main purpose of this paper is to introduce the notions of γ-operation, pre-open soft multisets, α-open multisets, semi-open soft multisets, β-open soft multisets and b-open soft multisets in soft multi topological spaces. In addition, the relationships among these types are studied. Moreover, the concepts of pre-soft multi continuous, α-soft multi continuous, semi-soft multi continuous, β-soft multi continuous and b-soft multi continuous functions are introduced and their properties are studied in detail. Also, the concepts of pre-soft (respectively semi-soft, α-soft, β-soft, b-soft) multi irresolute functions are presented.
Journal of Polytechnic, 2018
The purpose of this paper is to introduce new structures of -soft sets in soft ditopological (SDT) spaces and study -soft operations such as -soft interior, -soft closure, -soft boundary and -soft exterior. This study is therefore organized the analogies between the concepts of -soft operations, on the other, are strongly emphasized. Moreover, a result which play a pivotal role in the characterization of -soft open sets is found out.
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.
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.
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.
2018
Conditions related to bounds on the relations between soft spaces appear to be rare in the literature. In this paper, I study the notion of soft ditopology relates to the soft topology. Firstly, the soft ditopology via soft set theory is developed by de…ning soft ditopological subspace. Secondly, properties concerning to soft interior and soft closure are presented in soft ditopological subspace. In conclusion, soft subspaces of soft topology and soft ditopology being coincident have been proved, whence it is readily inferred that soft ditopological subspace can be obtained from soft topological subspace.
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