scholarly journals NEW SEPARATION AXIOMS VIA *GENERALIZED PRE OPEN SETS

2014 ◽  
Vol 1 (2) ◽  
pp. 16-19
Author(s):  
Kavitha P.R
Keyword(s):  
Topological Spaces ◽  
Basic Properties ◽  
Separation Axioms ◽  
Weak Separation

In this Paper, we introduce the notion of *g-p open sets and *g-p continuity in topological spaces. By tilizing these notions we introduce some weak separation axioms. Also we show that some basic properties of (*g, p)-Ti, (*g, p)-Di spaces, for i = 0, 1, 2,…

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 Some New Separation Axioms Via β-I-Open Sets

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
N. Gowrisankar ◽  
A. Keskin ◽  
N. Rajesh
Keyword(s):  
Basic Properties ◽  
Separation Axioms ◽  
Weak Separation

Abstract In this paper, β-I-open sets are used to define some weak separation axioms and to study some of their basic properties. The implications of these axioms among themselves and with the known axioms are investigated

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 types of -Open Sets and Associated Weak Separation Axioms

2016 ◽  
Vol 12 (2) ◽  
pp. 5862-5869
Author(s):  
Mohammed El Sharkasy
Keyword(s):  
Topological Spaces ◽  
Separation Axioms ◽  
Weak Separation

Pal and Bhattacharyya (1996)introduced the notion of pre--open sets.In this paper, we consider the class of pre--open sets in topological spaces and investigate some of their properties. Also,we present and study some weak separation axiomsby involving the notion of pre--open sets.

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 Separation Axioms of Interval-Valued Fuzzy Soft Topology via Quasi-Neighborhood Structure

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 178
Author(s):  
Mabruka Ali ◽  
Adem Kılıçman ◽  
Azadeh Zahedi Khameneh
Keyword(s):  
Topological Spaces ◽  
Neighborhood Structure ◽  
Basic Properties ◽  
Soft Topology ◽  
Separation Axioms ◽  
Soft Point ◽  
Interval Valued

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

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.

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