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2019, arXiv: General Topology
In 1999, Molodtsov initiated the concept of Soft Sets Theory as a new mathematical tool and a completely different approach for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the theory of soft topological spaces, also defining and investigating many new soft properties as generalization of the classical ones. In this paper, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Lemma for soft topological spaces.
https://arxiv.org/abs/1905.13050, 2019
In 1999, Molodtsov initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the notion of soft topological spaces, also defining and investigating many new soft properties as generalization of the classical ones. In this paper, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Lemma to the class of soft topological spaces.
2020
In this paper, based on the researches on soft set theory and soft topology, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Theorem to the class of soft topological spaces.
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.
2019
In this paper, we introduce and study some new soft properties namely, soft R0 and soft R1(SRi, for short i = 0, 1) by using the concept of distinct soft points and we obtain some of their properties. We show how they relate to some soft separation axioms in [21]. Also we, show that the properties SR0, SR1 are special cases of soft regularity. We further, show that in the case of soft compact spaces, SR1 is equivalent to soft regularity. Finally, the relations between these properties in soft topologies and that in crisp topologies are studied. Moreover, some counterexamples are given.
2015
Many scientists have studied and improved the soft set theory, which is initiated by Molodtsov (33) and easily applied to many problems having uncertainties from social life. The main purpose of our paper, is to introduce new soft separation axioms based on the b-open soft sets which are more general than of the open soft sets. We show that, the properties of soft b-Ti-spaces (i = 1, 2) are soft topological properties under the bijection and irr esolute open soft mapping. Also, the property of being soft b-regular and soft b-normal are soft topological properties under bijection, irresolute soft and irresolute open soft functions. Furthe r, we show that the properties of being soft b-Ti-spaces (i = 1, 2, 3, 4) are hereditary properties.
In the present paper, we introduce soft generalized closed sets in soft topological spaces which are defined over an initial universe with a fixed set of parameters. A sufficient condition for a soft g-closed set to be a soft closed is also presented. Moreover, the union and intersection of two soft g-closed sets are discussed. Finally, the new soft separation axiom, namely soft 1 2 T -space is introduced and its basic properties are investigated.
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.
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.
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.
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.
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.
TURKISH JOURNAL OF MATHEMATICS, 2019
This study aims to contribute to the theoretical studies on near soft sets and near soft topological spaces. In addition, it presents basic concepts and constructs that will form the basis for a near theoretical setup of near soft sets. These concepts and structures include near soft point, near soft interior, near soft closure, near soft neighborhood, near soft continuity, and near soft open (closed) function.
2017
In this paper, we introduce and investigate some weak soft separation axioms by using the notion of supra open soft sets, which is a generalization of the soft (resp. semi soft, pre soft, α-soft and β-soft separation axioms. We study the relationships between these new soft separation axioms and their relationships with some other properties.
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.
2019
Fuzzy soft separation axioms was introduced by Mahanta and Das ([5]) using the definitions of a `fuzzy soft point' and `the complement of a fuzzy soft point is a fuzzy soft point', and `distinct of fuzzy soft points' in there sense. In this paper we, introduce fuzzy soft separation axioms in terms of the modified definitions of a `fuzzy soft point', the complement of a fuzzy soft point is a fuzzy soft set' and `distinct of fuzzy soft points'([7]). Also, we study some of their properties. Finally, we discuss fuzzy soft topological property for such spaces.
gazi university journal of science, 2014
Arockiarani and Lancy (7), defined soft preopen (c losed) sets on soft topology. In this paper, we are continue investigating the properties of soft preopen (clos ed) sets and define soft preclosure and soft preinterior in soft topological spaces. We are also introduce and research basic properties of the concepts of soft prere gular spaces, soft P ₃�spaces, soft prenormal spaces and soft P ₄�spaces in soft topological spaces, which are basic for further research on soft topology and will fortify the footing of the theory of soft topological space.
2015
This paper focuses on soft $\pi$gb-closed sets and soft $\pi$gb-open sets in soft topological spaces and to investigate its properties. Further soft $\pi$gb-T1/2 space is introduced and its basic properties are discussed.
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.
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.
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.
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