Bipolar soft ordered topology and A New Definition for Bipolar Soft Topology

In this study, the concept of neutrosophic soft bitopological space is defined and it is one of the few studies that have dealt with this concept. In addition, pairwise neutrosophic soft open (closed) set on neutrosophic soft bitopological spaces are studied. Supra neutrosophic soft topology is defined by pairwise neutrosophic soft open sets. Important theorems related to the subject supported with many examples for a better understanding of the subject are given.

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Dual Fuzzy Soft Topology and Dual Fuzzy Soft Algebra

International Journal of Mathematics Trends and Technology ◽

10.14445/22315373/ijmtt-v66i2p514 ◽

2020 ◽

Vol 66 (2) ◽

pp. 121-125

Author(s):

Majd Hamid Mahmood

Keyword(s):

Soft Topology

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Homeomorphism and Quotient Mappings in Infrasoft Topological Spaces

Journal of Mathematics ◽

10.1155/2021/3388288 ◽

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.

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Infra Soft Compact Spaces and Application to Fixed Point Theorem

Journal of Function Spaces ◽

10.1155/2021/3417096 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Tareq M. Al-shami

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Topological Properties ◽

Finite Product ◽

Finite Intersection ◽

Compact Spaces ◽

Closed Sets ◽

Soft Topology ◽

Covering Properties

Infra soft topology is one of the recent generalizations of soft topology which is closed under finite intersection. Herein, we contribute to this structure by presenting two kinds of soft covering properties, namely, infra soft compact and infra soft Lindelöf spaces. We describe them using a family of infra soft closed sets and display their main properties. With the assistance of examples, we mention some classical topological properties that are invalid in the frame of infra soft topology and determine under which condition they are valid. We focus on studying the “transmission” of these concepts between infra soft topology and classical infra topology which helps us to discover the behaviours of these concepts in infra soft topology using their counterparts in classical infra topology and vice versa. Among the obtained results, these concepts are closed under infra soft homeomorphisms and finite product of soft spaces. Finally, we introduce the concept of fixed soft points and reveal main characterizations, especially those induced from infra soft compact spaces.

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Infra Soft Semiopen Sets and Infra Soft Semicontinuity

Journal of Function Spaces ◽

10.1155/2021/5716876 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Tareq M. Al-shami ◽

A. A. Azzam

Keyword(s):

Soft Set ◽

Finite Product ◽

Finite Intersection ◽

Soft Topology ◽

Continuous Mappings

To contribute to the area of infra soft topology, we introduce one of the generalizations of infra soft open sets called infra soft semiopen sets. We establish some characterizations of them and study their main properties. We determine under what condition this class is closed under finite intersection and show that this class is preserved under infra soft continuous mappings and finite product of soft spaces. Then, we present the concepts of infra semi-interior, infra semiclosure, infra semilimit, and infra semiboundary soft points of a soft set and elucidate the relationships between them. Finally, we exploit infra soft semiopen and infra soft semiclosed sets to define new types of soft mappings. We characterize each one of these soft mappings and explore main features.

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Methodological remarks on soft topology

Soft Computing ◽

10.1007/s00500-021-05587-7 ◽

2021 ◽

Vol 25 (5) ◽

pp. 4149-4156

Author(s):

Milan Matejdes

Keyword(s):

Soft Topology

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α -CONNECTEDNESS BETWEEN SOFT SETS

International Journal of Students Research in Technology & Management ◽

10.18510/ijsrtm.2019.742 ◽

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.

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