µ-Generalized closed sets via hereditary class in generalized topological space

2020 ◽  
Vol 33 (03) ◽  
Author(s):  
MANJEET SINGH ◽  
◽  
ASHA GUPTA ◽  
Keyword(s):  
Topological Space ◽  
Closed Sets ◽  
Hereditary Class ◽  
Generalized Topological Space

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.

Δμ-sets and ∇μ-sets in generalized topological spaces

2017 ◽  
Vol 24 (3) ◽  
pp. 403-407
Author(s):  
Pon Jeyanthi ◽  
Periadurai Nalayini ◽  
Takashi Noiri
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
Generalized Topological Space

AbstractIn this paper, we introduce and study some properties of the sets, namely {\Delta_{\mu}}-sets, {\nabla_{\mu}}-sets and {\Delta_{\mu}^{*}}-closed sets in a generalized topological space.

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.

scholarly journals Theory of g-Tg-Derived and g-Tg-Coderived Operators: Definitions, Essential Properties, Iterations, and Ranks

2020 ◽  
Author(s):  
Mohammad Irshad KHODABOCUS ◽  
Noor-Ul-Hacq SOOKIA
Keyword(s):  
Topological Space ◽  
Closure Operators ◽  
Closed Sets ◽  
Essential Properties ◽  
Generalized Topological Space ◽  
Delta G ◽  
Transfinite Recursion

In a generalized topological space Tg = (Ω, Tg) (Tg-space), the g-topology Tg : P (Ω) −→ P (Ω) can be characterized in the generalized sense by specifying the generalized open, generalized closed sets (g-Tg-open, g-Tg-closed sets), generalized interior, generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω) (g-Tg-interior, g-Tg-closure operators), or generalized derived, generalized coderived operators g-Derg, g-Codg : P (Ω) −→ P (Ω) (g-Tg-derived, g-Tg-coderived operators), respectively. For very many Tg-spaces, the δth-iterates g-Derg(δ), g-Codg(δ) : P (Ω) −→ P (Ω) of g-Derg, g-Codg : P (Ω) −→ P (Ω), respectively, defined by transfinite recursion on the class of successor ordinals are also themselves g-Tg-derived, g-Tg-coderived operators for new g-topologies in the generalized sense on Ω. Thus, the use of novel definitions of g-Tg-derived, g-Tg-coderived operators g-Derg, g-Codg : P (Ω) −→ P (Ω), respectively, based on a very clever construction, together with their δth-iterates g-Tg-operators g-Derg(δ), g-Codg(δ) : P (Ω) −→ P (Ω), defined by transfinite recursion on the class of successor ordinals, will give rise to novel generalized g-topologies on Ω. The present authors have been actively engaged in the study of g-Tg-operators in Tg-spaces. The study of the essential properties and the commutativity of novel definitions of g-Tg-interior and g-Tg-closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in Tg has formed the first part, and the study of the essential properties and sets of consistent, independent axioms of novel definitions of g-Tg-exterior and g-Tg-frontier operators g-Extg, g-Frg : P (Ω) −→ P (Ω), respectively, has formed the second part. In this work, which forms the last part on the theory of g-Tg-operators in Tg-spaces, the present authors propose to present novel definitions and the study of the essential properties of g-Tg-derived and g-Tg-coderived operators g-Derg, g-Codg : P (Ω) −→ P (Ω), respectively, and their δth-iterates, and the notions of g-Tg-open and g-Tg-closed sets of ranks δ in Tg-spaces.

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 Λµ- sets and V µ- sets in generalized topological spaces

2017 ◽  
Vol 35 (1) ◽  
pp. 33
Author(s):  
P Jeyanthi ◽  
P Nalayini ◽  
T Noiri
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
Generalized Topological Space

In this paper, we introduce and study some properties of the new sets namely * Λµ- sets , * V µ- sets, * λµ- closed sets, * λµ- open sets in generalized topological space.

Uniformity on generalized topological spaces

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Dipankar Dey ◽  
Dhananjay Mandal ◽  
Manabendra Nath Mukherjee
Keyword(s):  
Topological Space ◽  
Present Article ◽  
Design Methodology ◽  
Original Work ◽  
Generalized Topology ◽  
Topological Spaces ◽  
Intermediate Structure ◽  
Content Type ◽  
Completely Regular ◽  
Generalized Topological Space

PurposeThe present article deals with the initiation and study of a uniformity like notion, captioned μ-uniformity, in the context of a generalized topological space.Design/methodology/approachThe existence of uniformity for a completely regular topological space is well-known, and the interrelation of this structure with a proximity is also well-studied. Using this idea, a structure on generalized topological space has been developed, to establish the same type of compatibility in the corresponding frameworks.FindingsIt is proved, among other things, that a μ-uniformity on a non-empty set X always induces a generalized topology on X, which is μ-completely regular too. In the last theorem of the paper, the authors develop a relation between μ-proximity and μ-uniformity by showing that every μ-uniformity generates a μ-proximity, both giving the same generalized topology on the underlying set.Originality/valueIt is an original work influenced by the previous works that have been done on generalized topological spaces. A kind of generalization has been done in this article, that has produced an intermediate structure to the already known generalized topological spaces.

Quasihomeomorphisms and Skula spaces

2021 ◽  
Author(s):  
Othman Echi
Keyword(s):  
Topological Space ◽  
Alternative Proof ◽  
Manuscripta Math ◽  
Alexandroff Space ◽  
Closed Sets ◽  
Locally Closed Sets ◽  
Reflection Formula

Let [Formula: see text] be a topological space. By the Skula topology (or the [Formula: see text]-topology) on [Formula: see text], we mean the topology [Formula: see text] on [Formula: see text] with basis the collection of all [Formula: see text]-locally closed sets of [Formula: see text], the resulting space [Formula: see text] will be denoted by [Formula: see text]. We show that the following results hold: (1) [Formula: see text] is an Alexandroff space if and only if the [Formula: see text]-reflection [Formula: see text] of [Formula: see text] is a [Formula: see text]-space. (2) [Formula: see text] is a Noetherian space if and only if [Formula: see text] is finite. (3) If we denote by [Formula: see text] the Alexandroff extension of [Formula: see text], then [Formula: see text] if and only if [Formula: see text] is a Noetherian quasisober space. We also give an alternative proof of a result due to Simmons concerning the iterated Skula spaces, namely, [Formula: see text]. A space is said to be clopen if its open sets are also closed. In [R. E. Hoffmann, Irreducible filters and sober spaces, Manuscripta Math. 22 (1977) 365–380], Hoffmann introduced a refinement clopen topology [Formula: see text] of [Formula: see text]: The indiscrete components of [Formula: see text] are of the form [Formula: see text], where [Formula: see text] and [Formula: see text] is the intersection of all open sets of [Formula: see text] containing [Formula: see text] (equivalently, [Formula: see text]). We show that [Formula: see text]

Neutrosophic Nano Ideal Topological Structures

2018 ◽  
Author(s):  
Parimala Mani ◽  
Karthika M ◽  
jafari S ◽  
Smarandache F ◽  
Ramalingam Udhayakumar
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Structures ◽  
Basic Properties ◽  
Closed Sets ◽  
Structural Space ◽  
New Type

Neutrosophic nano topology and Nano ideal topological spaces induced the authors to propose this new concept. The aim of this paper is to introduce a new type of structural space called neutrosophic nano ideal topological spaces and investigate the relation between neutrosophic nano topological space and neutrosophic nano ideal topological spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.

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