scholarly journals On r -Generalized Fuzzy ℓ -Closed Sets: Properties and Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
I. M. Taha
Keyword(s):  
Topological Space ◽  
Closed Set ◽  
Closed Sets ◽  
Separation Axioms ◽  
Connected Sets ◽  
Fuzzy Ideal

In the present study, we introduce and characterize the class of r -generalized fuzzy ℓ -closed sets in a fuzzy ideal topological space X , τ , ℓ in Šostak sense. Also, we show that r -generalized fuzzy closed set by Kim and Park (2002) ⟹ r -generalized fuzzy ℓ -closed set, but the converse need not be true. Moreover, if we take ℓ = ℓ 0 , the r -generalized fuzzy ℓ -closed set and r -generalized fuzzy closed set are equivalent. After that, we define fuzzy upper (lower) generalized ℓ -continuous multifunctions, and some properties of these multifunctions along with their mutual relationships are studied with the help of examples. Finally, some separation axioms of r -generalized fuzzy ℓ -closed sets are introduced and studied. Also, the notion of r -fuzzy G ∗ -connected sets is defined and studied with help of r -generalized fuzzy ℓ -closed sets.

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.

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 Fine Fuzzy sp Closed Sets in Fine Fuzzy Topological Spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 1306-1313
Keyword(s):  
Continuous Function ◽  
Topological Space ◽  
Inverse Image ◽  
Continuous Functions ◽  
Topological Spaces ◽  
The Novel ◽  
Closed Set ◽  
Closed Sets ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The main view of this article is the extended version of the fine topological space to the novel kind of space say fine fuzzy topological space which is developed by the notion called collection of quasi coincident of fuzzy sets. In this connection, fine fuzzy closed sets are introduced and studied some features on it. Further, the relationship between fine fuzzy closed sets with certain types of fine fuzzy closed sets are investigated and their converses need not be true are elucidated with necessary examples. Fine fuzzy continuous function is defined as the inverse image of fine fuzzy closed set is fine fuzzy closed and its interrelations with other types of fine fuzzy continuous functions are obtained. The reverse implication need not be true is proven with examples. Finally, the applications of fine fuzzy continuous function are explained by using the composition.

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 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.

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 Fuzzy tgp-closed sets and fuzzy t^* gp-closed sets

2018 ◽  
Vol 7 (4.36) ◽  
pp. 718
Author(s):  
Noor Riyadh Kareem ◽  
. .
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Closed Set ◽  
Closed Sets ◽  
Fuzzy Topological Space

In this paper, we aim to address the idea of fuzzy -set and fuzzy -set in fuzzy topological space to present new types of the fuzzy closed set named fuzzy -closed set and fuzzy -closed set. We will study several examples and explain the relations of them with other classes of fuzzy closed sets. Moreover, in a fuzzy locally indiscrete space we can see that these two sets are the same.  

scholarly journals Vague Separation

2018 ◽  
Vol 7 (3.34) ◽  
pp. 654
Author(s):  
R Ramya Swetha ◽  
T Anitha ◽  
V Amarendra Babu
Keyword(s):  
Topological Space ◽  
Limit Point ◽  
Cartesian Product ◽  
Closed Set ◽  
Closed Sets ◽  
Derived Set ◽  
Isolated Point

In this paper we are introducing  VT1 space, vague haussdorff space (VT2) and then we derive every vague subspace of  VT1 space is VT1 and also for VT2. And also we derive the Cartesian product of two vague closed sets is also vague closed set in the vague product topological space X x Y .Finally we define Vague limit point, Vague isolated point, Vague adherent point, Vague perfect, Vague derived set, vague exterior and also derive some theorems on this .

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