scholarly journals More on D α -Closed Sets in Topological Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xiao-Yan Gao ◽  
Ahmed Mostafa Khalil
Keyword(s):  
Topological Spaces ◽  
Topological Properties ◽  
Closed Sets ◽  
Open Set ◽  
Separation Axioms

The aim of this paper is to present and study topological properties of D α -derived, D α -border, D α -frontier, and D α -exterior of a set based on the concept of D α -open sets. Then, we introduce new separation axioms (i.e., D α − R 0 and D α − R 1 ) by using the notions of D α -open set and D α -closure. The space of D α − R 0 (resp., D α − R 1 ) is strictly between the spaces of α − R 0 (resp., α − R 1 ) and g − R 0 (resp., g − R 1 ). Further, we present the notions of D α -kernel and D α -convergent to a point and discuss the characterizations of interesting properties between D α -closure and D α -kernel. Finally, several properties of weakly D α − R 0 space are investigated.

scholarly journals Certain new classes of generalized closed sets and their applications in ideal topological spaces

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1113-1120
Author(s):  
Dhananjoy Mandal ◽  
M.N. Mukherjee
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Set ◽  
Closed Sets ◽  
Open Set ◽  
Separation Axioms

In this paper, a type of closed sets, called *-g-closed sets, is introduced and studied in an ideal topological space. The class of such sets is found to lie strictly between the class of all closed sets and that of generalized closed sets of Levine [5]. We give some applications of *-g-closed set and *-g-open set in connection with certain separation axioms.

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

scholarly journals On Soft Separation Axioms and Their Applications on Decision-Making Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
T. M. Al-shami
Keyword(s):  
Decision Making ◽  
Topological Spaces ◽  
Topological Properties ◽  
Finite Product ◽  
Separation Axioms ◽  
Decision Making Problem ◽  
Weak Structure

In this work, we introduce new types of soft separation axioms called p t -soft α regular and p t -soft α T i -spaces i = 0,1,2,3,4 using partial belong and total nonbelong relations between ordinary points and soft α -open sets. These soft separation axioms enable us to initiate new families of soft spaces and then obtain new interesting properties. We provide several examples to elucidate the relationships between them as well as their relationships with e -soft T i , soft α T i , and t t -soft α T i -spaces. Also, we determine the conditions under which they are equivalent and link them with their counterparts on topological spaces. Furthermore, we prove that p t -soft α T i -spaces i = 0,1,2,3,4 are additive and topological properties and demonstrate that p t -soft α T i -spaces i = 0,1,2 are preserved under finite product of soft spaces. Finally, we discuss an application of optimal choices using the idea of p t -soft T i -spaces i = 0,1,2 on the content of soft weak structure. We provide an algorithm of this application with an example showing how this algorithm is carried out. In fact, this study represents the first investigation of real applications of soft separation axioms.

scholarly journals Soft Simply Compact Spaces

2020 ◽  
pp. 108-113
Author(s):  
S. Noori ◽  
Y. Y. Yousif
Keyword(s):  
Topological Spaces ◽  
Compact Spaces ◽  
Open Set ◽  
Separation Axioms

The aim of this research is to use the class of soft simply open set to define new types of separation axioms in soft topological spaces. We also introduce and study the concept of soft simply compactness.

scholarly journals Relations of Pre Generalized Regular Weakly Locally Closed Sets in Topological Spaces

2021 ◽  
Vol 12 (3) ◽  
pp. 3444-3454
Author(s):  
Vijayakumari T Et.al
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Set ◽  
Closed Sets ◽  
Open Set ◽  
Continuous Maps ◽  
Locally Closed Sets

In this paper pgrw-locally closed set, pgrw-locally closed*-set and pgrw-locally closed**-set are introduced. A subset A of a topological space (X,t) is called pgrw-locally closed (pgrw-lc) if A=GÇF where G is a pgrw-open set and F is a pgrw-closed set in (X,t). A subset A of a topological space (X,t) is a pgrw-lc* set if there exist a pgrw-open set G and a closed set F in X such that A= GÇF. A subset A of a topological space (X,t) is a pgrw-lc**-set if there exists an open set G and a pgrw-closed set F such that A=GÇF. The results regarding pgrw-locally closed sets, pgrw-locally closed* sets, pgrw-locally closed** sets, pgrw-lc-continuous maps and pgrw-lc-irresolute maps and some of the properties of these sets and their relation with other lc-sets are established.

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.

Characterizations of \(\theta\)-closed sets using separation axioms in ideal topological spaces

2017 ◽  
Vol 8 (2) ◽  
pp. 159
Author(s):  
Navpreet Singh Noorie ◽  
Nitakshi Goyal
Keyword(s):  
Topological Spaces ◽  
Closed Sets ◽  
Separation Axioms

We will give various characterizations of \(\theta\)-closed sets with respect to an ideal using separation axioms. Also give its relationship with other type of closed sets defined in literature.  

On ΛIs-sets and the related notions in ideal topological spaces

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
José Sanabria ◽  
Ennis Rosas ◽  
Carlos Carpintero
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
Separation Axioms

AbstractIn this paper, we define and study the notions of ΛIs-sets, ΛIs-closed sets and I-generalized semi-closed (briefly I-gs-closed) sets by using semi-I-open sets in an ideal topological space. Moreover, we present and characterize two new low separation axioms using the above notions.

scholarly journals Some separation axioms in generalized topological spaces

2011 ◽  
Vol 31 (1) ◽  
pp. 29
Author(s):  
V. Pankajam ◽  
Diraviam Sivaraj
Keyword(s):  
Topological Spaces ◽  
Closed Sets ◽  
Separation Axioms

We give different definitions for g-closed sets, R_0, and R_1 spaces in generalized topological spaces, characterize such spaces and compare with the existing results.

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