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 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.

A View on Fuzzy Minimal Open Sets and Fuzzy Maximal Open Sets

2015 ◽  
Vol 7 (1) ◽  
pp. 62-73 ◽  
Author(s):  
Hamid Reza Moradi
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Basic Properties ◽  
New Class ◽  
Properties And Characterization ◽  
Open Set ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Characterization Theorems

A nonzero fuzzy open set () of a fuzzy topological space is said to be fuzzy minimal open (resp. fuzzy maximal open) set if any fuzzy open set which is contained (resp. contains) in is either or itself (resp. either or itself). In this note, a new class of sets called fuzzy minimal open sets and fuzzy maximal open sets in fuzzy topological spaces are introduced and studied which are subclasses of open sets. Some basic properties and characterization theorems are also to be investigated.

Neutrosophic Nano Ideal Topological Structures

2018 ◽  
Author(s):  
Parimala Mani ◽  
Karthika M ◽  
jafari S ◽  
Smarandache F ◽  
Ramalingam Udhayakumar
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Structures ◽  
Basic Properties ◽  
Closed Sets ◽  
Structural Space ◽  
New Type

Neutrosophic nano topology and Nano ideal topological spaces induced the authors to propose this new concept. The aim of this paper is to introduce a new type of structural space called neutrosophic nano ideal topological spaces and investigate the relation between neutrosophic nano topological space and neutrosophic nano ideal topological spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.

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 Basic Properties of Metrizable Topological Spaces

2009 ◽  
Vol 17 (3) ◽  
pp. 201-205 ◽  
Author(s):  
Karol Pąk
Keyword(s):  
Topological Space ◽  
General Topology ◽  
Topological Spaces ◽  
Basic Properties ◽  
Special Case

Basic Properties of Metrizable Topological Spaces We continue Mizar formalization of general topology according to the book [11] by Engelking. In the article, we present the final theorem of Section 4.1. Namely, the paper includes the formalization of theorems on the correspondence between the cardinalities of the basis and of some open subcover, and a discreet (closed) subspaces, and the weight of that metrizable topological space. We also define Lindelöf spaces and state the above theorem in this special case. We also introduce the concept of separation among two subsets (see [12]).

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 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.

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.

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