scholarly journals Some new separation axioms in fuzzy soft topological spaces

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1775-1783
Author(s):  
Islam Taha
Keyword(s):  
Topological Space ◽  
Topological Property ◽  
Topological Spaces ◽  
Hereditary Property ◽  
Invariance Properties ◽  
Separation Axioms ◽  
New Form ◽  
Soft Topological Space

In this paper, a new form of separation axioms called r-fuzzy soft Ti;(i = 0,1,2,3,4), r-fuzzy soft regular and r-fuzzy soft normal axioms are introduced in a fuzzy soft topological space based on the paper Ayg?no?lu et al. [7]. Also, the relations of these axioms with each other are investigated with the help of examples. Furthermore, some fuzzy soft invariance properties, namely fuzzy soft topological property and hereditary property are specified.

scholarly journals Weaker Forms of Soft Regular and Soft T2 Soft Topological Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2153
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Topological Property ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Soft Topological Space

Soft ω-local indiscreetness as a weaker form of both soft local countability and soft local indiscreetness is introduced. Then soft ω-regularity as a weaker form of both soft regularity and soft ω-local indiscreetness is defined and investigated. Additionally, soft ω-T2 as a new soft topological property that lies strictly between soft T2 and soft T1 is defined and investigated. It is proved that soft anti-local countability is a sufficient condition for equivalence between soft ω-locally indiscreetness (resp. soft ω-regularity) and soft locally indiscreetness (resp. soft ω-regularity). Additionally, it is proved that the induced topological spaces of a soft ω-locally indiscrete (resp. soft ω-regular, soft ω-T2) soft topological space are (resp. ω-regular, ω-T2) topological spaces. Additionally, it is proved that the generated soft topological space of a family of ω-locally indiscrete (resp. ω-regular, ω-T2) topological spaces is soft ω-locally indiscrete and vice versa. In addition to these, soft product theorems regarding soft ω-regular and soft ω-T2 soft topological spaces are obtained. Moreover, it is proved that soft ω-regular and soft ω-T2 are hereditarily under soft subspaces.

scholarly journals Co-Compact Separation Axioms and Slight Co-Continuity

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1614
Author(s):  
Samer Al Ghour ◽  
Enas Moghrabi
Keyword(s):  
Topological Space ◽  
Topological Property ◽  
Closed Subspace ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Compact Sets ◽  
Separation Axioms ◽  
Preservation Theorems

Via co-compact open sets we introduce co-T2 as a new topological property. We show that this class of topological spaces strictly contains the class of Hausdorff topological spaces. Using compact sets, we characterize co-T2 which forms a symmetry. We show that co-T2 propoerty is preserved by continuous closed injective functions. We show that a closed subspace of a co-T2 topological space is co-T2. We introduce co-regularity as a weaker form of regularity, s-regularity as a stronger form of regularity and co-normality as a weaker form of normality. We obtain several characterizations, implications, and examples regarding co-regularity, s-regularity and co-normality. Moreover, we give several preservation theorems under slightly coc-continuous functions.

scholarly journals Partial soft separation axioms and soft compact spaces

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4755-4771 ◽  
Author(s):  
M.E. El-Shafei ◽  
M. Abo-Elhamayel ◽  
T.M. Al-Shami
Keyword(s):  
Topological Space ◽  
General Topology ◽  
Regular Space ◽  
Topological Spaces ◽  
Finite Product ◽  
Compact Spaces ◽  
Separation Axioms ◽  
Soft Topological Space

The main aim of the present paper is to define new soft separation axioms which lead us, first, to generalize existing comparable properties via general topology, second, to eliminate restrictions on the shape of soft open sets on soft regular spaces which given in [22], and third, to obtain a relationship between soft Hausdorff and new soft regular spaces similar to those exists via general topology. To this end, we define partial belong and total non belong relations, and investigate many properties related to these two relations. We then introduce new soft separation axioms, namely p-soft Ti-spaces (i = 0,1,2,3,4), depending on a total non belong relation, and study their features in detail. With the help of examples, we illustrate the relationships among these soft separation axioms and point out that p-soft Ti-spaces are stronger than soft Ti-spaces, for i = 0,1,4. Also, we define a p-soft regular space, which is weaker than a soft regular space and verify that a p-soft regular condition is sufficient for the equivalent among p-soft Ti-spaces, for i = 0,1,2. Furthermore, we prove the equivalent among finite p-soft Ti-spaces, for i = 1,2,3 and derive that a finite product of p-soft Ti-spaces is p-soft Ti, for i = 0,1,2,3,4. In the last section, we show the relationships which associate some p-soft Ti-spaces with soft compactness, and in particular, we conclude under what conditions a soft subset of a p-soft T2-space is soft compact and prove that every soft compact p-soft T2-space is soft T3-space. Finally, we illuminate that some findings obtained in general topology are not true concerning soft topological spaces which among of them a finite soft topological space need not be soft compact.

scholarly journals Hereditary properties of semi-separation axioms and their applications

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4689-4700 ◽  
Author(s):  
Sang-Eon Han
Keyword(s):  
Topological Space ◽  
Infinite Product ◽  
Topological Spaces ◽  
Hereditary Property ◽  
Separation Axiom ◽  
Product Property ◽  
Low Level ◽  
Separation Axioms ◽  
Hereditary Properties

The paper studies the open-hereditary property of semi-separation axioms and applies it to the study of digital topological spaces such as an n-dimensional Khalimsky topological space, a Marcus-Wyse topological space and so on. More precisely, we study various properties of digital topological spaces related to low-level and semi-separation axioms such as T1/2 , semi-T1/2 , semi-T1, semi-T2, etc. Besides, using the finite or the infinite product property of the semi-Ti-separation axiom, i ? {1,2}, we prove that the n-dimensional Khalimsky topological space is a semi-T2-space. After showing that not every subspace of the digital topological spaces satisfies the semi-Ti-separation axiom, i ?{1,2}, we prove that the semi-Tiseparation property is open-hereditary, i ? {1,2}. All spaces in the paper are assumed to be nonempty and connected.

scholarly journals Separation Axioms in Intuitionistic Fuzzy Topological Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Amit Kumar Singh ◽  
Rekha Srivastava
Keyword(s):  
Topological Space ◽  
Left Adjoint ◽  
Topological Spaces ◽  
Intuitionistic Fuzzy ◽  
Separation Axioms ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

In this paper we have studied separation axiomsTi,i=0,1,2in an intuitionistic fuzzy topological space introduced by Coker. We also show the existence of functorsℬ:IF-Top→BF-Topand𝒟:BF-Top→IF-Topand observe that𝒟is left adjoint toℬ.

scholarly journals Fuzzyθ-closure operator on fuzzy topological spaces

1991 ◽  
Vol 14 (2) ◽  
pp. 309-314 ◽  
Author(s):  
M. N. Mukherjee ◽  
S. P. Sinha
Keyword(s):  
Topological Space ◽  
Fuzzy Sets ◽  
Closure Operator ◽  
Topological Spaces ◽  
Separation Axioms ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The paper contains a study of fuzzyθ-closure operator,θ-closures of fuzzy sets in a fuzzy topological space are characterized and some of their properties along with their relation with fuzzyδ-closures are investigated. As applications of these concepts, certain functions as well as some spaces satisfying certain fuzzy separation axioms are characterized in terms of fuzzyθ-closures andδ-closures.

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 A Class of Separation Axioms in Generalized Topology

2016 ◽  
Vol 4 (2) ◽  
pp. 151-159
Author(s):  
D Anabalan ◽  
Santhi C
Keyword(s):  
Topological Space ◽  
Generalized Topology ◽  
Regular Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
New Class ◽  
Separation Axioms ◽  
Generalized Topological Space

The purpose of this paper is to introduce and study some new class of definitions like µ-point closure and gµ –regular space concerning generalized topological space. We obtain some characterizations and several properties of such definitions. This paper takes some investigations on generalized topological spaces with gµ –closed sets and gµ–closed sets.

A note on nano g #α-closed maps in nano topological spaces

2020 ◽  
pp. 539-548
Author(s):  
S. Visagapriya ◽  
V. Kokilavani
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
Separation Axioms

The point of this article is to show separation axioms of Nano $g^{\#} \alpha$ closed sets in nano topological space. We moreover present and explore nano $g^{\#} \alpha$-closed maps and additionally consider their principal properties.

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.

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