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 Soft Semi ω-Open Sets

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3168
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closure Operators ◽  
Closed Sets ◽  
Soft Topology ◽  
Locally Countable ◽  
Soft Topological Space

In this paper, we introduce the class of soft semi ω-open sets of a soft topological space (X,τ,A), using soft ω-open sets. We show that the class of soft semi ω-open sets contains both the soft topology τω and the class of soft semi-open sets. Additionally, we define soft semi ω-closed sets as the class of soft complements of soft semi ω-open sets. We present here a study of the properties of soft semi ω-open sets, especially in (X,τ,A) and (X,τω,A). In particular, we prove that the class of soft semi ω-open sets is closed under arbitrary soft union but not closed under finite soft intersections; we also study the correspondence between the soft topology of soft semi ω-open sets of a soft topological space and their generated topological spaces and vice versa. In addition to these, we introduce the soft semi ω-interior and soft semi ω-closure operators via soft semi ω-open and soft semi ω-closed sets. We prove several equations regarding these two new soft operators. In particular, we prove that these operators can be calculated using other usual soft operators in both of (X,τ,A) and (X,τω,A), and some equations focus on soft anti-locally countable soft topological spaces.

scholarly journals Bioperators on soft topological spaces

2021 ◽  
Vol 6 (11) ◽  
pp. 12471-12490
Author(s):  
Baravan A. Asaad ◽  
◽  
Tareq M. Al-shami ◽  
Abdelwaheb Mhemdi ◽  
◽  
...  
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
Fundamental Properties ◽  
Soft Topology ◽  
Open Set ◽  
Soft Topological Space

<abstract><p>To contribute to soft topology, we originate the notion of soft bioperators $ \tilde{\gamma} $ and $ {\tilde{\gamma}}^{'} $. Then, we apply them to analyze soft $ (\tilde{\gamma}, {\tilde{\gamma}}^{'}) $-open sets and study main properties. We also prove that every soft $ (\tilde{\gamma}, {\tilde{\gamma}}^{'}) $-open set is soft open; however, the converse is true only when the soft topological space is soft $ (\tilde{\gamma}, {\tilde{\gamma}}^{'}) $-regular. After that, we define and study two classes of soft closures namely $ Cl_{(\tilde{\gamma}, {\tilde{\gamma}}^{'})} $ and $ \tilde{\tau}_{(\tilde{\gamma}, {\tilde{\gamma}}^{'})} $-$ Cl $ operators, and two classes of soft interior namely $ Int_{(\tilde{\gamma}, {\tilde{\gamma}}^{'})} $ and $ \tilde{\tau}_{(\tilde{\gamma}, {\tilde{\gamma}}^{'})} $-$ Int $ operators. Moreover, we introduce the notions of soft $ (\tilde{\gamma}, {\tilde{\gamma}}^{'}) $-$ g $.closed sets and soft $ (\tilde{\gamma}, {\tilde{\gamma}}^{'}) $-$ T_{\frac{1}{2}} $ spaces, and explore their fundamental properties. In general, we explain the relationships between these notions, and give some counterexamples.</p></abstract>

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.

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 e#-open and *e-open sets via -open sets

2021 ◽  
Vol 12 (2) ◽  
pp. 2125-2128
Author(s):  
V. Amsaveni, Et. al.
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closure Operators ◽  
Closed Sets

The notion of -open sets in a topological space was studied by Velicko.  Usha Parmeshwari et.al. and Indira et.al. introduced the concepts of b# and *b open sets respectively. Following this Ekici et. al. studied the notions of e-open and e-closed sets by mixing the closure, interior, -interior and -closure operators.  In this paper some new sets namely e#-open and *e-open sets are defined and their relationship with other similar concetps in topological spaces will be investigated.

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 Sum of Soft Topological Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 990 ◽  
Author(s):  
Tareq M. Al-shami ◽  
Ljubiša D. R. Kočinac ◽  
Baravan A. Asaad
Keyword(s):  
Topological Space ◽  
Pairwise Disjoint ◽  
Topological Spaces ◽  
Basic Properties ◽  
Boundary Points ◽  
Soft Limit ◽  
Soft Topological Space

In this paper, we introduce the concept of sum of soft topological spaces using pairwise disjoint soft topological spaces and study its basic properties. Then, we define additive and finitely additive properties which are considered a link between soft topological spaces and their sum. In this regard, we show that the properties of being p-soft T i , soft paracompactness, soft extremally disconnectedness, and soft continuity are additive. We provide some examples to elucidate that soft compactness and soft separability are finitely additive; however, soft hyperconnected, soft indiscrete, and door soft spaces are not finitely additive. In addition, we prove that soft interior, soft closure, soft limit, and soft boundary points are interchangeable between soft topological spaces and their sum. This helps to obtain some results related to some important generalized soft open sets. Finally, we observe under which conditions a soft topological space represents the sum of some soft topological spaces.

scholarly journals On Vietoris Soft Topology I

2016 ◽  
Vol 8 (1) ◽  
pp. 13-19
Author(s):  
Q. R. Shakir
Keyword(s):  
Topological Space ◽  
Closed Sets ◽  
Soft Topology ◽  
The Impact ◽  
Soft Topological Space

 In this article, we define the hyperspace of soft closed sets of a soft topological space (FA, ?). In addition, we define the Vietoris soft topology, ?v, by determining the soft base of this topology which has the form ?FH1, FH2,.....FHn?, where ?FH1, FH2,.....FHn? are soft open sets in (FA, ?). Some properties of this topology are also investigated. The impact of introducing the Vietoris soft topology is to enable us to understand many properties of the structure of soft topologies corresponding to it.

scholarly journals Soft ωp-Open Sets and Soft ωp-Continuity in Soft Topological Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2632
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Strong Form ◽  
Topological Spaces ◽  
New Class ◽  
Soft Topology ◽  
Dense Sets ◽  
Soft Topological Space

We define soft ωp-openness as a strong form of soft pre-openness. We prove that the class of soft ωp-open sets is closed under soft union and do not form a soft topology, in general. We prove that soft ωp-open sets which are countable are soft open sets, and we prove that soft pre-open sets which are soft ω-open sets are soft ωp-open sets. In addition, we give a decomposition of soft ωp-open sets in terms of soft open sets and soft ω-dense sets. Moreover, we study the correspondence between the soft topology soft ωp-open sets in a soft topological space and its generated topological spaces, and vice versa. In addition to these, we define soft ωp-continuous functions as a new class of soft mappings which lies strictly between the classes of soft continuous functions and soft pre-continuous functions. We introduce several characterizations for soft pre-continuity and soft ωp-continuity. Finally, we study several relationships related to soft ωp-continuity.

scholarly journals On topological soft sets

2020 ◽  
Vol 16 (2) ◽  
pp. 5-22
Author(s):  
M. Burç Kandemir ◽  
B. Tanay
Keyword(s):  
Topological Space ◽  
Structural Properties ◽  
Soft Set ◽  
Point Of View ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Soft Sets ◽  
Closed Sets ◽  
Necessary And Sufficient

AbstractIn 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.

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