scholarly journals ON SEPARATION AXIOMS IN TOPOLGICAL SPACES

2016 ◽  
Vol 4 (6) ◽  
pp. 163-169
Author(s):  
Mahesh Bhat ◽  
Hanif PAGE
Keyword(s):  
Topological Spaces ◽  
Closed Sets ◽  
Separation Axioms ◽  
Weak Separation

The purpose of this paper is to introduce weak separation axioms via sgp-closed sets in topological spaces and study some of their properties.

scholarly journals Applications of operations on generalized topological spaces

2021 ◽  
Vol 103 (3) ◽  
pp. 96-104
Author(s):  
B. Roy ◽  
◽  
T. Noiri
Keyword(s):  
Closure Operator ◽  
Topological Spaces ◽  
Closure Operators ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
Separation Axioms ◽  
Weak Separation ◽  
General Collection ◽  
Generalized Type

In this paper γµ -open sets and γµ -closed sets in a GTS (X, µ) have been studied, where γµ is an operation from µ to P(X). In general, collection of γµ -open sets is smaller than the collection of µ-open sets. The condition under which both are same are also established here. Some properties of such sets have been discussed. Some closure like operators are also defined and their properties are discussed. The relation between similar types of closure operators on the GTS (X, µ) has been established. The condition under which the newly defined closure like operator is a Kuratowski closure operator is given. We have also defined a generalized type of closed sets termed as γµ -generalized closed set with the help of this newly defined closure operator and discussed some basic properties of such sets. As an application, we have introduced some weak separation axioms and discussed some of their properties. Finally, we have shown some preservation theorems of such generalized concepts.

scholarly journals On generalized γµ-closed sets and related continuity

2021 ◽  
Vol 13 (2) ◽  
pp. 483-493
Author(s):  
Ritu Sen
Keyword(s):  
Topological Space ◽  
Main Interest ◽  
Closed Sets ◽  
Separation Axioms ◽  
Preservation Theorems ◽  
Generalized Topological Space ◽  
New Type ◽  
Weak Separation

Abstract In this paper our main interest is to introduce a new type of generalized open sets defined in terms of an operation on a generalized topological space. We have studied some properties of this newly defined sets. As an application, we have introduced some weak separation axioms and discussed some of their properties. Finally, we have studied some preservation theorems in terms of some irresolute functions.

scholarly journals Minimal TUD spaces

2002 ◽  
Vol 3 (1) ◽  
pp. 55 ◽  
Author(s):  
A.E. McCluskey ◽  
W.S. Watson
Keyword(s):  
Topological Space ◽  
Partial Order ◽  
Linear Order ◽  
Closed Sets ◽  
Separation Axioms ◽  
Derived Set ◽  
Weak Separation

<p>A topological space is T<sub>UD</sub> if the derived set of each point is the union of disjoint closed sets. We show that there is a minimal T<sub>UD</sub> space which is not just the Alexandroff topology on a linear order. Indeed the structure of the underlying partial order of a minimal T<sub>UD</sub> space can be quite complex. This contrasts sharply with the known results on minimality for weak separation axioms.</p>

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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