scholarly journals On Two Classes of Soft Sets in Soft Topological Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 265 ◽  
Author(s):  
Samer Al Ghour ◽  
Worood Hamed
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Logical Connective ◽  
Soft Sets ◽  
Natural Properties ◽  
Soft Topological Space

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

2019 ◽  
Vol 7 (4) ◽  
pp. 09-14
Author(s):  
Alpa Singh Rajput ◽  
S. S. Thakur
Keyword(s):  
Image Processing ◽  
Image Segmentation ◽  
Topological Space ◽  
Topological Spaces ◽  
Soft Sets ◽  
Soft Topology ◽  
Feasible Path ◽  
Soft Topological Space

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.

scholarly journals A Review of Fuzzy Soft Topological Spaces, Intuitionistic Fuzzy Soft Topological Spaces and Neutrosophic Soft Topological Spaces

2020 ◽  
pp. 96-104
Author(s):  
admin admin ◽  
◽  
◽  
◽  
M M.Karthika ◽  
...  
Keyword(s):  
Topological Space ◽  
Fuzzy Sets ◽  
Topological Structure ◽  
Intuitionistic Fuzzy Set ◽  
Soft Set ◽  
Topological Spaces ◽  
Soft Sets ◽  
Structure Space ◽  
Intuitionistic Fuzzy ◽  
Soft Topological Space

The notion of fuzzy sets initiated to overcome the uncertainty of an object. Fuzzy topological space, in- tuitionistic fuzzy sets in topological structure space, vagueness in topological structure space, rough sets in topological space, theory of hesitancy and neutrosophic topological space, etc. are the extension of fuzzy sets. Soft set is a family of parameters which is also a set. Fuzzy soft topological space, intuitionistic fuzzy soft and neutrosophic soft topological space are obtained by incorporating soft sets with various topological structures. This motivates to write a review and study on various soft set concepts. This paper shows the detailed review of soft topological spaces in various sets like fuzzy, Intuitionistic fuzzy set and neutrosophy. Eventually, we compared some of the existing tools in the literature for easy understanding and exhibited their advantages and limitations.

scholarly journals Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1781
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Soft Sets ◽  
New Concepts ◽  
Bitopological Spaces ◽  
The Relationship ◽  
Soft Topological Space

In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give several sufficient conditions for the equivalence between soft p-open sets and each of the soft u-open sets and soft s-open sets, respectively. In addition to these, we introduce the soft u-ω-open, soft p-ω-open, and soft s-ω-open sets as three new classes of soft sets in soft bitopological spaces, which contain soft u-open sets, soft p-open sets, and soft s-open sets, respectively. Via soft u-open sets, we define two notions of Lindelöfeness in SBTSs. We discuss the relationship between these two notions, and we characterize them via other types of soft sets. We define several types of soft local countability in soft bitopological spaces. We discuss relationships between them, and via some of them, we give two results related to the discrete soft topological space. According to our new concepts, the study deals with the correspondence between soft bitopological spaces and their generated bitopological spaces.

scholarly journals SOFT α-COMPACTNESS VIA SOFT IDEALS

2016 ◽  
Vol 12 (4) ◽  
pp. 6178-6184 ◽  
Author(s):  
A A Nasef ◽  
A E Radwan ◽  
F A Ibrahem ◽  
R B Esmaeel
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Properties ◽  
Soft Topological Space

In the present paper, we have continued to study the properties of soft topological spaces. We introduce new types of soft compactness based on the soft ideal Ĩ in a soft topological space (X, τ, E) namely, soft αI-compactness, soft αI-Ĩ-compactness, soft α-Ĩ-compactness, soft α-closed, soft αI-closed, soft countably α-Ĩ-compactness and soft countably αI-Ĩ-compactness. Also, several of their topological properties are investigated. The behavior of these concepts under various types of soft functions has obtained

scholarly journals Bipolar Soft Topological Spaces

2020 ◽  
Vol 13 (2) ◽  
pp. 227-245
Author(s):  
Asmaa Fadel ◽  
Syahida Che Dzul-Kifli
Keyword(s):  
Set Theory ◽  
Soft Set ◽  
The Other ◽  
Topological Spaces ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Positive Information ◽  
Soft Limit ◽  
Soft Point ◽  
Soft Topological Space

Bipolar soft set theory is a mathematical tool associates between bipolarity and soft set theory, it is defined by two soft sets one of them gives us the positive information where the other gives us the negative. The goal of our paper is to define the bipolar soft topological space on a bipolar soft set and study its basic notions and properties. We also investigate the definitions of: bipolar soft interior, bipolar soft closure, bipolar soft exterior, bipolar soft boundary and establish some important properties on them. Some relations between them are also discussed. Moreover, the notions of bipolar soft point, bipolar soft limit point and the derived set of a bipolar soft set are discussed. In additions, examples are presented to illustrate our work.

scholarly journals On Soft Topological Space via Semiopen and Semiclosed Soft Sets

2014 ◽  
Vol 54 (2) ◽  
pp. 221-236 ◽  
Author(s):  
Juthika Mahanta ◽  
Pramod Kumar Das
Keyword(s):  
Topological Space ◽  
Soft Sets ◽  
Soft Topological Space

scholarly journals New Soft Structure: Infra Soft Topological Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Tareq M. Al-shami
Keyword(s):  
Topological Space ◽  
Soft Set ◽  
Topological Spaces ◽  
Closure Operators ◽  
Relative Topology ◽  
Closed Sets ◽  
Soft Topology ◽  
Soft Limit ◽  
Basic Concepts ◽  
Soft Topological Space

It is always convenient to find the weakest conditions that preserve some topologically inspired properties. To this end, we introduce the concept of an infra soft topology which is a collection of subsets that extend the concept of soft topology by dispensing with the postulate that the collection is closed under arbitrary unions. We study the basic concepts of infra soft topological spaces such as infra soft open and infra soft closed sets, infra soft interior and infra soft closure operators, and infra soft limit and infra soft boundary points of a soft set. We reveal the main properties of these concepts with the help of some elucidative examples. Then, we present some methods to generate infra soft topologies such as infra soft neighbourhood systems, basis of infra soft topology, and infra soft relative topology. We also investigate how we initiate an infra soft topology from crisp infra topologies. In the end, we explore the concept of continuity between infra soft topological spaces and determine the conditions under which the continuity is preserved between infra soft topological space and its parametric infra topological spaces.

scholarly journals The Net in a Fuzzy Soft Topological Space and Its Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Rui Gao ◽  
Jianrong Wu
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Soft Topological Space

In this paper, the fuzzy soft net is explored to study the properties of a fuzzy soft topological space. Some important results about the closure, separation, and compactness are obtained. It is demonstrated that the net is a powerful tool for studying fuzzy soft topological spaces.

scholarly journals Soft idealization of a decomposition theorem

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 741-751 ◽  
Author(s):  
Yunus Yumak ◽  
Aynur Kaymakcı
Keyword(s):  
Topological Space ◽  
Decomposition Theorem ◽  
Topological Spaces ◽  
Closed Set ◽  
Soft Topological Space ◽  
Regular Closed

Firstly, we define a new set called soft regular-?-closed set in soft ideal topological spaces and obtain some properties of it. Secondly, to obtain a decomposition of continuity in these spaces, we introduce two notions of soft Hayashi-Samuels space and soft A?-set. Finally, we give a decomposition of continuity in a domain Hayashi-Samuels space and in a range soft topological space.

scholarly journals Soft Open Bases and a Novel Construction of Soft Topologies from Bases for Topologies

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 672 ◽  
Author(s):  
José Carlos R. Alcantud
Keyword(s):  
Topological Space ◽  
General Construction ◽  
Topological Spaces ◽  
Soft Sets ◽  
Extensive Discussion ◽  
Soft Topology

Soft topology studies a structure on the collection of all soft sets on a given set of alternatives (the relevant attributes being fixed). It is directly inspired by the axioms of a topological space. This paper contributes to the theoretical bases of soft topology in various ways. We extend a general construction of soft topologies from topologies on the set of alternatives in two different directions. An extensive discussion with criteria about what a soft counterpart of “topological separability” should satisfy is also given. The interactions of the properties that arise with separability, and of second-countability and its soft counterpart, are studied under the general mechanisms that generate soft topological spaces. The first non-trivial examples of soft second-countable soft topological spaces are produced as a consequence.

Sign in / Sign up

Export Citation Format

Share Document