scholarly journals On β-local Functions in Ideal topological Spaces

2020 ◽  
Vol 13 (4) ◽  
pp. 758-765
Author(s):  
Pournima Powar ◽  
Takashi Noiri ◽  
Shikha Bhadauria
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Local Function ◽  
Closed Sets ◽  
Local Functions

In this paper, by using β-open sets in [1] we introduce and investigate the conceptsof the β-local function, Is∗g-β-closed sets and Ig-β-closed sets in an ideal topological space. In addition to the properties, an operation cl∗β is defined and the properties are obtained similarly with the local function in [8].

scholarly journals Soft Semi Local Functions in Soft Ideal Topological Spaces

2019 ◽  
Vol 12 (3) ◽  
pp. 857-869
Author(s):  
Fatouh Gharib ◽  
Alaa Mohamed Abd El-latif
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Local Function ◽  
Soft Sets ◽  
Soft Topology ◽  
Local Functions ◽  
Equivalent Conditions

In this paper, we define a soft semi local function (F, E) ∗s ( ˜I, τ ) by using semi open soft sets in a soft ideal topological space (X, τ, E, ˜I). This concept is discussed with a view to find new soft topologies from the original one, called ∗s-soft topology. Some properties and characterizations of soft semi local function are explored. Finally, the notion of soft semi compatibility of soft ideals with soft topologies is introduced and some equivalent conditions concerning this topic are established here.

scholarly journals Fuzzy Ideal Supra Topological Spaces

2020 ◽  
Author(s):  
Fadhil Abbas
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Basic Structure ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Local Function ◽  
Closed Sets ◽  
Fuzzy Ideal ◽  
Neighbourhood Structure

Abstract In this paper, we introduce the notion of fuzzy ideals in fuzzy supra topological spaces. The concept of a fuzzy s-local function is also introduced here by utilizing the s-neighbourhood structure for a fuzzy supra topological space. These concepts are discussed with a view to nd new fuzzy supra topologies from the original one. The basic structure, especially a basis for such generated fuzzy supra topologies and several relations between different fuzzy ideals and fuzzy supra topologies are also studied here. Moreover, we introduce a fuzzy set operator ΨS and study its properties. Finally, we introduce some sets of fuzzy ideal supra topological spaces (fuzzy *-supra dense-in-itself sets, fuzzy S*-supra closed sets, fuzzy *-supra perfect sets, fuzzy regular-I-supra closed sets, fuzzy-I-supra open sets, fuzzy semi-I-supra open sets, fuzzy pre-I-supra open sets, fuzzy α-I-supra open sets, fuzzy β-I-supra open sets) and study some characteristics of theses sets and then we introduce some fuzzy ideal supra continuous functions.

scholarly journals Second approximation of local functions in ideal topological spaces

2019 ◽  
Vol 22 (2) ◽  
pp. 245-256 ◽  
Author(s):  
Md. Monirul Islam ◽  
Shyamapada Modak
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Local Function ◽  
Local Functions

This paper gives a new dimension to discuss the local function in ideal topological spaces. We calculate error operators for various type of local functions and introduce more perfect approximation of the local functions for discussing their properties. We have also reached a topological space with the help of semi-closure.

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.

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 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 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.

Pre-Local Function in Ideal Topological Spaces

2021 ◽  
Vol 8 (1) ◽  
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Local Function

The aim of this paper is to introduce the notation of pre-local function A^(p^* )(I, ?) by using pre-open sets in an ideal topological space (X, ?, I). Some properties and characterizations of a pre-local function are explored Pre-compatible spaces are also defined and investigated. Moreover, by using A^(p^* )(I, ?) we introduce an operator ?: P(X)?? satisfying ?(A) = X-?(X-A)?^(p^* )for each A ? P(X) and we discuss some characterizations this operator by use pre-open sets.

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