A Study on Neutro-Topological Neighbourhood and Neutro-Topological Base

Abstract

Recently, Smarandache introduced NeutroAlgebra and AntiAlgebras. NeutroAlgebras and AntiAlgebras represent a new research subject that is based on real-world examples. He studied the concept of neutro-structures and anti-structures. From the concepts of NeutroAlgebra, he showed that if a statement (theorem, lemma, consequence, property, etc.) is totally true in a classical Algebra, it does not mean that it is also totally true in a NeutroAlgebra or an AntiAlgebra. It depends on the operations and axioms (if they are totally true, partially true, totally false, or partially or totally indeterminate) it is based upon. In this study, the concept of Neutro-Topological neighbourhood and Neutro-Topological base are studied. Some examples of Neutro-Neighbourhood and Neutro-Base are given and compare the results of classical topological neighbourhood and Neutro-Topological Neighbourhood as well as classical topological base and Neutro-Topological Base.