scholarly journals A NEW TYPE OF CLUSTER SETS AND ITS APPLICATIONS

1995 ◽  
Vol 26 (4) ◽  
pp. 327-336
Author(s):  
M. N. MUKHERJEE ◽  
S. RAYCHAUDHURI
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Cluster Sets ◽  
New Type ◽  
Func Tion

In this paper we introduce the concept of a new type of cluster sets, termed $\delta$-cluster sets, of functions and multifunctions between topological spaces. Expressions of such sets are found and multifunctions with $\delta$-closed graphs are characterized. Also the behaviour of $\delta$-cluster sets toward a-continuity of a func- tion is observed. Finally as applications, we find new characterizations of almost regularity, near compactness and near Lindelofness of a topological space in terms of $\delta$-cluster sets of suitable multifunctions.

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.

scholarly journals Theory of g-Tg-Connectedness

2018 ◽  
Author(s):  
Mohammad Irshad Khodabocus ◽  
Noor-Ul-Hacq Sookia
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Starting Point ◽  
Generalized Topological Space ◽  
New Type

Several specific types of ordinary and generalized connectedness in a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new type of generalized connectedness in a generalized topological space is reported herein as a starting point for more generalized types.

scholarly journals OnS-cluster sets andS-closed spaces

2000 ◽  
Vol 23 (9) ◽  
pp. 597-603 ◽  
Author(s):  
M. N. Mukherjee ◽  
Atasi Debray
Keyword(s):  
Explicit Expression ◽  
New Technique ◽  
Topological Spaces ◽  
Cluster Set ◽  
Cluster Sets ◽  
New Type ◽  
A New Technique

A new type of cluster sets, calledS-cluster sets, of functions and multifunctions between topological spaces is introduced, thereby providing a new technique for studyingS-closed spaces. The deliberation includes an explicit expression ofS-cluster set of a function. As an application, characterizations of Hausdorff andS-closed topological spaces are achieved via such cluster sets.

scholarly journals Pre Separation Axioms In Neutrosophic Crisp Topological Spaces

2020 ◽  
pp. 72-79
Author(s):  
Riad K. Al Al-Hamido ◽  
◽  
◽  
◽  
Luai Salha ◽  
...  
Keyword(s):  
Topological Space ◽  
The Other ◽  
Topological Spaces ◽  
Open Set ◽  
Separation Axioms ◽  
New Type

In this paper, A new type of separation axioms in the neutrosophic crisp Topological space named neutrosophic crisp pre separation axioms is going to be defined , in which neutrosophic crisp pre open set and neutrosophic crisp point are to be depended on. Also, relations among them and the other type are going to be found.

scholarly journals Lacunary distributional convergence in topological spaces

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4297-4306
Author(s):  
Havva Uluçay ◽  
Mehmet Ünver
Keyword(s):  
Topological Space ◽  
Group Structure ◽  
Lacunary Sequence ◽  
Distribution Functions ◽  
Topological Spaces ◽  
Hausdorff Topological Space ◽  
Lacunary Sequences ◽  
Summability Methods ◽  
Borel Field ◽  
New Type

Most of the summability methods cannot be defined in an arbitrary Hausdorff topological space unless one introduces a linear or a group structure. In the present paper, using distribution functions over the Borel ?-field of the topology and lacunary sequences we define a new type of convergencemethod in an arbitrary Hausdorff topological space and we study some inclusion theorems with respect to the resulting summability method. We also investigate the inclusion relation between lacunary sequence and lacunary refinement of it.

The Ra operator in ideal topological spaces

2016 ◽  
Vol 25 (1) ◽  
pp. 1-10
Author(s):  
WADEI FARIS AL-OMERI ◽  
◽  
MOHD. SALMI MD. NOORANI ◽  
T. NOIRI ◽  
A. AL-OMARI ◽  
...  
Keyword(s):  
Topological Space ◽  
Ideal Space ◽  
Topological Spaces ◽  
Local Function ◽  
New Type ◽  
The Ideal

Given a topological space (X, τ) an ideal I on X and A ⊆ X, the concept of a-local function is defined as follows Aa ∗ (I, τ) = {x ∈X : U ∩ A /∈ I, for every U ∈ τ a(x)}. In this paper a new type of space has been introduced with the help of a-open sets and the ideal topological space called a-ideal space. We introduce an operator <a : ℘(X) → τ, for every A ∈ ℘(X), and we use it to define some interesting generalized a-open sets and study their properties.

scholarly journals Antisymmetry of the Stochastical Order on all Ordered Topological Spaces

2019 ◽  
Vol 7 (1) ◽  
pp. 250-252 ◽  
Author(s):  
Tobias Fritz
Keyword(s):  
Topological Space ◽  
General Result ◽  
Elementary Proof ◽  
Short Note ◽  
Stochastic Order ◽  
Topological Spaces ◽  
Probability Measures ◽  
Ordered Topological Space ◽  
Special Cases

Abstract In this short note, we prove that the stochastic order of Radon probability measures on any ordered topological space is antisymmetric. This has been known before in various special cases. We give a simple and elementary proof of the general result.

On topological quotient maps preserved by pullbacks or products

1970 ◽  
Vol 67 (3) ◽  
pp. 553-558 ◽  
Author(s):  
B. J. Day ◽  
G. M. Kelly
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Quotient Maps ◽  
Continuous Maps

We are concerned with the category of topological spaces and continuous maps. A surjection f: X → Y in this category is called a quotient map if G is open in Y whenever f−1G is open in X. Our purpose is to answer the following three questions:Question 1. For which continuous surjections f: X → Y is every pullback of f a quotient map?Question 2. For which continuous surjections f: X → Y is f × lz: X × Z → Y × Z a quotient map for every topological space Z? (These include all those f answering to Question 1, since f × lz is the pullback of f by the projection map Y ×Z → Y.)Question 3. For which topological spaces Z is f × 1Z: X × Z → Y × Z a qiptoent map for every quotient map f?

scholarly journals Separation Axioms in Intuitionistic Fuzzy Topological Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Amit Kumar Singh ◽  
Rekha Srivastava
Keyword(s):  
Topological Space ◽  
Left Adjoint ◽  
Topological Spaces ◽  
Intuitionistic Fuzzy ◽  
Separation Axioms ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

In this paper we have studied separation axiomsTi,i=0,1,2in an intuitionistic fuzzy topological space introduced by Coker. We also show the existence of functorsℬ:IF-Top→BF-Topand𝒟:BF-Top→IF-Topand observe that𝒟is left adjoint toℬ.

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.

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