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On Product of Smooth Neutrosophic Topological Spaces

On Product of Smooth Neutrosophic Topological Spaces
Author: Kalaivani Chandran
Publisher: Infinite Study
Total Pages: 20
Release: 2020-09-21
Genre: Mathematics
ISBN:

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In this paper, we develop the notion of the basis for a smooth neutrosophic topology in a more natural way. As a sequel, we define the notion of symmetric neutrosophic quasi-coincident neighborhood systems and prove some interesting results that fit with the classical ones, to establish the consistency of theory developed. Finally, we define and discuss the concept of product topology, in this context, using the definition of basis.


On Neutrosophic Semi-Open sets in Neutrosophic Topological Spaces

On Neutrosophic Semi-Open sets in Neutrosophic Topological Spaces
Author: P. Iswarya
Publisher: Infinite Study
Total Pages: 10
Release:
Genre:
ISBN:

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The purpose of this paper is to define the product related neutrosophic topological space and proved some theorems based on this. We introduce the concept of neutrosophic semiopen sets and neutrosophic semi-closed sets in neutrosophic topological spaces and derive some of their characterization. Finally, we analyze neutrosophic semi-interior and neutrosophic semi-closure operators also.


Neutrosophic Pre-open Sets and Pre-closed Sets in Neutrosophic Topology

Neutrosophic Pre-open Sets and Pre-closed Sets in Neutrosophic Topology
Author: V. Venkateswara Rao
Publisher: Infinite Study
Total Pages: 10
Release:
Genre:
ISBN:

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The purpose of this article is to extend some more topics of topology in neutrosophic topology. Eerily introduce neutrosophic topological space and open sets, closed sets, semi-open and semi closed sets, now in this manuscript we extend up to neutrosophic pre-open and pre-closed (NPO and NPC).


A Study on Connectedness in Neutrosophic Topological Spaces

A Study on Connectedness in Neutrosophic Topological Spaces
Author: Ahu Acikgoz
Publisher: Infinite Study
Total Pages: 5
Release:
Genre: Mathematics
ISBN:

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In this study, we introduce the concept of neutrosophic connectedness and give some of its characterizations. Additionally, we present neutrosophic product space and show that this type of connectedness is not preserved under neutrosophic product spaces. We also introduce the notions of neutrosophic super-connected spaces, neutrosophic strongly connected spaces and study their properties.


On Neutrosophic Feebly Frontier in Neutrosophic Topological Spaces

On Neutrosophic Feebly Frontier in Neutrosophic Topological Spaces
Author: P. Jeya Puvaneswari
Publisher: Infinite Study
Total Pages: 6
Release:
Genre: Mathematics
ISBN:

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In this paper, we introduce a new class of operator using neutrosophic feebly closed sets namely neutrosophic feebly frontier. Also we study some of their basic properties and their characterizations.


Neutrosophic Topological Spaces

Neutrosophic Topological Spaces
Author: Murad Arar
Publisher: Infinite Study
Total Pages: 16
Release: 2020-12-01
Genre: Mathematics
ISBN:

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In this paper, the concept of neutrosophic topological spaces is introduced. We define and study the properties of neutrosophic open sets, closed sets, interior and closure. The set of all generalize neutrosophic pre-closed sets GNPC and the set of all neutrosophic open sets in a neutrosophic topological space can be considered as examples of generalized neutrosophic topological spaces.


Neutrosophic SuperHyperAlgebra and New Types of Topologies

Neutrosophic SuperHyperAlgebra and New Types of Topologies
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 254
Release: 2023-09-01
Genre: Mathematics
ISBN:

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In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P2(S) } and so on. That’s why the n-th PowerSet of a Set S { defined recursively and denoted by Pn(S) = P(Pn-1(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real world. The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology.


Neutrosophic Vague Topological Spaces

Neutrosophic Vague Topological Spaces
Author: Mary Margaret A.
Publisher: Infinite Study
Total Pages: 12
Release:
Genre: Mathematics
ISBN:

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The term topology was introduced by Johann Beredict Listing in the 19th century. Closed sets are fundamental objects in a topological space. In this paper, we use neutrosophic vague sets and topological spaces and we construct and develop a new concept namely “neutrosophic vague topological spaces”. By using the fundamental definition and necessary example we have defined the neutrosophic vague topological spaces and have also discussed some of its properties. Also we have defined the neutrosophic vague continuity and neutrosophic vague compact space in neutrosophic vague topological spaces and their properties are deliberated.


Ordinary Single Valued Neutrosophic Topological Spaces

Ordinary Single Valued Neutrosophic Topological Spaces
Author: Junhui Kim
Publisher: Infinite Study
Total Pages: 26
Release:
Genre: Mathematics
ISBN:

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We define an ordinary single valued neutrosophic topology and obtain some of its basic properties. In addition, we introduce the concept of an ordinary single valued neutrosophic subspace. Next, we define the ordinary single valued neutrosophic neighborhood system and we show that an ordinary single valued neutrosophic neighborhood system has the same properties in a classical neighborhood system. Finally, we introduce the concepts of an ordinary single valued neutrosophic base and an ordinary single valued neutrosophic subbase, and obtain two characterizations of an ordinary single valued neutrosophic base and one characterization of an ordinary single valued neutrosophic subbase.


On Neutrosophic Feebly Open Set In Neutrosophic Topological Spaces

On Neutrosophic Feebly Open Set In Neutrosophic Topological Spaces
Author: P. Jeya Puvaneswari
Publisher: Infinite Study
Total Pages: 8
Release:
Genre:
ISBN:

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The focus of this paper is to introduce the concept of Neutrosophic point, Neutrosophic quasi coincident, Neutrosophic feebly open sets and Neutrosophic feebly closed sets in Neutrosophic Topological spaces. Also we analyse their characterizations and investigate their properties. This concept is the generalization of intuitionistic topological spaces and fuzzy topological spaces. Using this neutrosophic feebly open sets and neutrosophic feebly closed sets, we define a new class of functions namely neutrosophic feebly continuous functions. Further, relationships between this new class and the other classes of functions are established.