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 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 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.

On separation axioms for certain types of ordered topological space

1977 ◽  
Vol 82 (1) ◽  
pp. 59-65 ◽  
Author(s):  
D. C. J. Burgess ◽  
M. Fitzpatrick
Keyword(s):  
Topological Space ◽  
Partial Order ◽  
Ordered Topological Space ◽  
Separation Axioms ◽  
Space Order ◽  
Order Separation

An ordered topological space (E, τ, ≥) is a set E endowed with a topology τ and a partial order ≥. For such a space order separation axioms have been studied by Nachbin (6) and McCartan (3). In this paper we discuss the consequences for these axioms of the imposition, in turn, of four conditions on (E, τ, ≥), namely convexity (6), continuity, anticontinuity and bicontinuity (5).

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 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 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.

Properties and Applications of d*g? - Closed Sets in Topological Spaces

2021 ◽  
Vol 7 (3) ◽  
Author(s):  
M. Vigneshwaran ◽  
S. Ranganayaki
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
Separation Axioms

We introduce the concept of d*g?-closed sets in a topological space and investigate their properties. Moreover, we investigate new separation axioms and new functions in topological spaces.

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