scholarly journals Homeomorphism and Quotient Mappings in Infrasoft Topological Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Tareq M. Al-shami
Keyword(s):  
Topological Spaces ◽  
Soft Topology ◽  
Quotient Mappings

In this paper, we contribute to infrasoft topology which is one of the recent generalizations of soft topology. Firstly, we redefine the concept of soft mappings to be convenient for studying the topological concepts and notions in different soft structures. Then, we introduce the concepts of open, closed, and homeomorphism mappings in the content of infrasoft topology. We establish main properties and investigate the transmission of these concepts between infrasoft topology and its parametric infratopologies. Finally, we define a quotient infrasoft topology and infrasoft quotient mappings and study their main properties with the aid of illustrative examples.

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 Separation Axioms Interval-Valued Fuzzy Soft Topology via Quasi-Neighbourhood Structure

2019 ◽  
Author(s):  
Mabruka Ali ◽  
Adem Kılıçman ◽  
Azadeh Zahedi Khameneh
Keyword(s):  
Topological Spaces ◽  
Basic Properties ◽  
Soft Topology ◽  
Separation Axioms ◽  
Neighbourhood Structure ◽  
Soft Point ◽  
Interval Valued

In this study, we present the concept of interval-valued fuzzy soft point and then introduce the notions of neighborhood and quasi-neighbourhood of it in interval-valued fuzzy soft topological spaces. Separation axioms in interval-valued fuzzy soft topology, so-called $q$-$T_{i}$ for $ i=0,1,2,3,4 ,$ is introduced and some of its basic properties are also studied.

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 Caliber and Chain Conditions in Soft Topologies

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2349
Author(s):  
José Carlos R. Alcantud ◽  
Tareq M. Al-shami ◽  
A. A. Azzam
Keyword(s):  
Future Research ◽  
Topological Spaces ◽  
Soft Sets ◽  
Theoretical Underpinning ◽  
Chain Conditions ◽  
Soft Topology ◽  
Uncertain Knowledge ◽  
Point Set ◽  
Fruitful Field

In this paper, we contribute to the growing literature on soft topology. Its theoretical underpinning merges point-set or classical topology with the characteristics of soft sets (a model for the representation of uncertain knowledge initiated in 1999). We introduce two types of axioms that generalize suitable concepts of soft separability. They are respectively concerned with calibers and chain conditions. We investigate explicit procedures for the construction of non-trivial soft topological spaces that satisfy these new axioms. Then we explore the role of cardinality in their study, and the relationships among these and other properties. Our results bring to light a fruitful field for future research in soft topology.

scholarly journals SOFT ALMOST β-CONTINUITY IN SOFT TOPOLOGICAL SPACES

2020 ◽  
Vol 8 (2) ◽  
pp. 06-14
Author(s):  
Alpa Singh Rajput ◽  
S. S. Thakur ◽  
Om Prakash Dubey
Keyword(s):  
Image Segmentation ◽  
Information Systems ◽  
Mathematical Models ◽  
General Framework ◽  
Continuous Mapping ◽  
Topological Spaces ◽  
Major Area ◽  
Soft Topology ◽  
Continuous Mappings

Purpose: In the present paper the concept of soft almost β-continuous mappings and soft almost β-open mappings in soft topological spaces have been introduced and studied. Methodology: This notion is weaker than both soft almost pre-continuous mappings, soft almost semi-continuous mapping. The diagrams of implication among these soft classes of soft mappings have been established. Main Findings: We extend the concept of almost β-continuous mappings and almost β-open mappings in soft topology. Implications: Mapping is an important and major area of topology and it can give many relationships between other scientific areas and mathematical models. This notion captures the idea of hanging-togetherness of image elements in an object by assigning strength of connectedness to every possible path between every possible pair of image elements. It is an important tool for the designing of algorithms for image segmentation. The novelty of Study: Hope that the concepts and results established in this paper will help the researcher to enhance and promote the further study on soft topology to carry out a general framework for the development of information systems.

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.

scholarly journals On Soft Metric Spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 6103-6110
Author(s):  
Radwa mohamed Hassan
Keyword(s):  
Mathematical Theory ◽  
General Framework ◽  
Metric Spaces ◽  
Topological Spaces ◽  
Topological Properties ◽  
Soft Sets ◽  
Soft Topology ◽  
Practical Life ◽  
Definition Of ◽  
Metric Function

After the famous article of Moldotsove [10] in 1999 which initiate the theory of soft sets as a mathematical theory to deal  with the uncertainty problems, many research works in the softbmathematics and its applications in various fields are appeared.   In [17], the authers introduced a new definition of the soft metric function using the soft elements. By this definition each soft metric in view of Das and Samanta [6] is also a soft metric in our concept but the converse is not true. In the present paper, some soft topological properties are given in details, namely (soft compactness, soft sequentially compactness, continuity and uniformly continues of soft functions between soft topological spaces).  We hope that the findings in thispaper will help researcher enhance and promote the further study on soft topology to carry out a general framework for theirapplications in practical life.

scholarly journals Soft Semi Local Functions in Soft Ideal Topological Spaces

2019 ◽  
Vol 12 (3) ◽  
pp. 857-869
Author(s):  
Fatouh Gharib ◽  
Alaa Mohamed Abd El-latif
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Local Function ◽  
Soft Sets ◽  
Soft Topology ◽  
Local Functions ◽  
Equivalent Conditions

In this paper, we define a soft semi local function (F, E) ∗s ( ˜I, τ ) by using semi open soft sets in a soft ideal topological space (X, τ, E, ˜I). This concept is discussed with a view to find new soft topologies from the original one, called ∗s-soft topology. Some properties and characterizations of soft semi local function are explored. Finally, the notion of soft semi compatibility of soft ideals with soft topologies is introduced and some equivalent conditions concerning this topic are established here.

scholarly journals Some Properties of Soft β-Connected Spaces in Soft Topological Spaces

2017 ◽  
Vol 18 ◽  
pp. 13-21
Author(s):  
S.S. Benchalli ◽  
Prakash Gouda Patil ◽  
Abeda S. Dodamani
Keyword(s):  
Set Theory ◽  
Soft Set ◽  
Theory And Practice ◽  
Topological Spaces ◽  
Soft Topology ◽  
Practical Life ◽  
Connected Spaces

Soft set theory is a newly emerging tool to deal with uncertain problems and has been studied by researchers in theory and practice. In this paper, we investigated the properties and characterizations of softβ-connected spaces in soft topological spaces. We anticipate that the results in this paper can be stimulated to the further study on soft topology to accomplish genenral framework for the practical life applications.

Sign in / Sign up

Export Citation Format

Share Document