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 .

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 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 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 On (μ1, μ2, μ3)-Weakly Generalized Closed Sets

2020 ◽  
Vol 13 (4) ◽  
pp. 977-986
Author(s):  
Breix Michael Agua ◽  
Rolando N. Paluga
Keyword(s):  
Topological Space ◽  
Closed Set ◽  
Closed Sets ◽  
Special Cases ◽  
Generalized Topological Space

This paper defines a new generalization of closed sets in a tri-generalized topological space called (μ1, μ2, μ3)-weakly generalized closed set (or briefly (μ1,μ2, μ3)-wg closed set) which is defined as follows: A subset A of X is (μ1, μ2, μ3)-weakly generalized closed set if clμ1(intμ2(A)) ⊆U whenever A ⊆ U and U is μ3-open in X. At least fifteen defined closed sets found in literature are considered special cases of (μ1, μ2, μ3)-weakly generalized closed set under some conditions. Furthermore, some properties of (μ1, μ2, μ3)-weakly generalized closed sets are obtained.

scholarly journals Semifield metric spaces

1969 ◽  
Vol 1 (1) ◽  
pp. 127-136
Author(s):  
Martin Kleiber ◽  
W. J. Pervin
Keyword(s):  
Topological Space ◽  
Metric Space ◽  
Metric Spaces ◽  
Product Representation ◽  
Closed Set ◽  
Completely Regular ◽  
Closed Sets ◽  
Directed Set

Extending the results of An†onovskiĭ, Bol†janskiĭ, and Sarymsakov on semifield metric spaces, the authors define a regular semifield metric to be one in which the distance in the standard Tychonoff product representation of a point from a disjoint closed set is nonzero. It is shown that every completely regular topological space possesses a completely regular semifield metric and that there is an equivalent completely regular semifield metric for every semifield metric space. A normal semifield metric is defined to be one in which the distance between two disjoint closed sets is nonzero and it is shown that possessing a normal semifield metric is equivalent to being a normal topological space. Finally, Cauchy nets in semifield metric spaces are introduced leading to the notion of completeness. It is shown that a semifield metric space is complete iff every Cauchy net with the property that its directed set has cardinality less than or equal to the cardinality of the indexing set of the Tychonoff product representation of the semifield converges.

Weak Normality and Related Properties

1970 ◽  
Vol 22 (5) ◽  
pp. 997-1001
Author(s):  
Eugene S. Ball
Keyword(s):  
Positive Integer ◽  
Topological Space ◽  
Closed Set ◽  
Common Part ◽  
Closed Sets ◽  
Open Set ◽  
Point Set ◽  
Weak Normality ◽  
Definition Of

In [5], Zenor stated the definition of weakly normal. In the main, since weak normality does not imply either normality or regularity, various properties related to either normality or regularity will be considered in the context of weak normality.Throughout this paper the word “space” will mean topological space. The closure of a point set M will be denoted by cl(M). The closure of a point set M with respect to the subspace K will be denoted by cl(M, K).Definition 1. A space S is weakly normal provided that if is a monotonically decreasing sequence of closed sets in S with no common part and H is a closed set in S not intersecting H1, then there is a positive integer N and an open set D such that HN ⊂ D and cl(D) does not intersect H.

scholarly journals NANO bT CLOSED SET IN NANO TOPOLOGICAL SPACES

2015 ◽  
Vol 2 (2) ◽  
pp. 26-29
Author(s):  
Krishnaveni K ◽  
Vigneshwaran M
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Set ◽  
Closed Sets ◽  
New Class

In this paper, we introduce a new class of set namely n a n o bT -closed sets in nano topological space. WealsodiscussedsomepropertiesofnanobTclosedset.

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