𝒢Θτi⋆τj-Fuzzy Closure Operator

2020 ◽  
Vol 16 (01) ◽  
pp. 123-141
Author(s):  
Fahad Alsharari ◽  
Yaser. M. Saber
Keyword(s):  
Closure Operator ◽  
Closed Sets ◽  
New Class ◽  
Continuous Mappings ◽  
Fuzzy Ideal ◽  
Bitopological Spaces

In this paper, a new class of fuzzy ideal sets, namely the [Formula: see text]-[Formula: see text]-[Formula: see text]-generalized fuzzy ideal closed sets, is introduced for fuzzy bitopological spaces in Šostak sense. This class falls strictly in between the class of [Formula: see text]-[Formula: see text]-[Formula: see text]-fuzzy ideal closed sets and the class of [Formula: see text]-[Formula: see text]-generalized fuzzy ideal closed sets. Furthermore, by using the class of [Formula: see text]-[Formula: see text]-[Formula: see text]-generalized fuzzy ideal closed sets we establish a new fuzzy closure operator which generates fuzzy bitopological spaces in Šostak sense. Finally, the [Formula: see text] strongly-[Formula: see text]-fuzzy ideal continuous, [Formula: see text]-[Formula: see text]-generalized fuzzy ideal continuous and [Formula: see text]-[Formula: see text]-generalized fuzzy ideal irresolute mappings are introduced, and we show the [Formula: see text]-[Formula: see text]-generalized fuzzy ideal continuous properly fuzzy ideal bitopological spaces in Šostak sense (for short, fibtss) in between [Formula: see text] strongly-[Formula: see text]-fuzzy ideal continuous and [Formula: see text]-generalized fuzzy continuous mappings.

Generalized Fuzzy Closed Sets in Smooth Bitopological Spaces

2016 ◽  
pp. 419-456
Author(s):  
Osama A. El-Tantawy ◽  
Sobhy A. El-Sheikh ◽  
Rasha N. Majeed
Keyword(s):  
Closure Operator ◽  
Closure Operators ◽  
Closed Sets ◽  
Different Types ◽  
Definition Of ◽  
Bitopological Spaces

This chapter is devoted to the study of r-generalized fuzzy closed sets (briefly, gfc sets) in smooth bitopological spaces (briefly, smooth bts) in view definition of Šostak (1985). The chapter is divided into seven sections. The aim of Sections 1-2 is to introduce the fundamental concepts related to the work. In Section 3, the concept of r-(ti,tj)-gfc sets in the smooth bts's is introduce and investigate some notions of these sets, generalized fuzzy closure operator induced from these sets. In Section 4, (i,j)-GF-continuous (respectively, irresolute) mappings are introduced. In Section 5, the supra smooth topology which generated from a smooth bts is used to introduce and study the notion of r-t12-gfc sets for smooth bts's and supra generalized fuzzy closure operator . The present notion of gfc sets and the notion which introduced in section 3, are independent. In Section 6, two types of generalized supra fuzzy closure operators introduced by using two different approaches. Finally, Section 7 introduces and studies different types of fuzzy continuity which are related to closure.

scholarly journals Theta - ω - Mappings in Topological Spaces

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Closure Operator ◽  
Topological Spaces ◽  
New Class ◽  
Continuous Mappings

In 2017 S. Ghour and B. Irshedat defined the θω - closure operator as a new topological operator and introduced θω - open sets as a new class of sets and proved that this class of sets is strictly between the class of open sets and the class of θ - open sets. In this paper we introduce θω - continuous, θω - irresolute, θω - open, θω - closed, pre - θω - open, θω - pre closed, contra θω - continuous and almost contra θω - continuous mappings and investigate properties and characterizations of these new types of mappings in topological spaces.

WEAKLY (1,2)$^{\ast}$-$\widetilde{g}$-CLOSED SETS IN BIOTOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9341-9344
Author(s):  
K. Prabhavathi ◽  
K. Nirmala ◽  
R.S. Kumar
Keyword(s):  
Closed Sets ◽  
New Class ◽  
Regular Open ◽  
Bitopological Spaces

The concept of bitopological spaces was first introduced by J.C. Kelly [2] in 1963. Regular open sets have been introduced and investigated by Stone [5]. In this paper, we introduce a new class of generalized closed sets called weakly (1,2)$^{\ast}$-$\widetilde{g}$-closed sets which contains the above mentioned class. Also, we investigate the relationships among the related generalized closed sets.

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.

On intuitionistic supra pre open sets

2020 ◽  
pp. 619-625
Author(s):  
L. Vidyarani ◽  
M. Jesintha
Keyword(s):  
Topological Spaces ◽  
Closed Sets ◽  
New Class

In this paper,a new class of sets called Intuitionistic Supra Pre open sets are defined in intuitionistic supra Topological spaces. Furthermore,the properties of Intuitionistic Supra Pre open sets and Intuitionistic Supra Pre closed sets are investigated in intuitionistic supra topological spaces.

scholarly journals Generalized ψ∗-closed sets in bitopological spaces

2015 ◽  
Vol 23 (3) ◽  
pp. 527-534 ◽  
Author(s):  
H.M. Abu Donia ◽  
M.A. Abd Allah ◽  
A.S. Nawar
Keyword(s):  
Closed Sets ◽  
Bitopological Spaces

scholarly journals New approach of ideal topological generalized closed sets

2013 ◽  
Vol 31 (2) ◽  
pp. 191
Author(s):  
Chinnapazham Santhini ◽  
M. Lellis Thivagar
Keyword(s):  
Continuous Functions ◽  
New Approach ◽  
Closed Sets ◽  
New Class

In this paper,we introduce and investigate the notions of Iˆω -closed sets andI ˆω -continuous functions,maximal Iˆω -closed sets and maximal Iˆω -continuous functionsin ideal topological spaces.We also introduce a new class of spaces calledMTˆω -spaces.

scholarly journals ON H˝-CLOSED SETS IN TOPOLOGICAL SPACES

2021 ◽  
Vol 9 (1) ◽  
pp. 1421-1424
Author(s):  
A. JOSE LITTLE FLOWER, M. RAJA KALAIVANAN
Keyword(s):  
Topological Spaces ◽  
Closed Sets ◽  
New Class

In this article, we introduce a new class of closed sets in topological spaces namely, H˝-closed and we prove every subset of the digital line is H˝-closed.

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