£-Single Valued Extremally Disconnected Ideal Neutrosophic Topological Spaces

Fahad Alsharari

doi:10.3390/sym13010053

Abstract

This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, the concepts of £-single valued neutrosophic extremally disconnected and £-single valued neutrosophic normal spaces are established. As a result, a useful implication diagram between the r-single valued neutrosophic ideal open sets is obtained. Finally, some kinds of separation axioms, namely r-single valued neutrosophic ideal-Ri (r-SVNIRi, for short), where i={0,1,2,3}, and r-single valued neutrosophic ideal-Tj (r-SVNITj, for short), where j={1,2,212,3,4}, are introduced. Some of their characterizations, fundamental properties, and the relations between these notions have been studied.

Highlights

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The family of all single-valued neutrosophic sets on Xis denoted by ξ X
We have introduced the definition of the r-single valued neutrosophic £closed and r-single valued neutrosophic £-open sets over single valued neutrosophic ideal topology space in Šostak’s sense

Summary

Introduction

In 1999, Smarandache introduced the concept of a neutrosophy [1] It has been used at various axes of mathematical theories and applications. In 1985 [8], marked out a new definition of fuzzy topology as a crisp subfamily of family of fuzzy sets, which seems to be a drawback in the process of fuzzification of the concept of topological spaces. This paper sets out to introduce and examine a new class of sets called r-single valued £-closed in the single valued neutrosophic topological spaces in Šostak’s sense. £-single valued neutrosophic normal spaces, and some kinds of separation axioms, were developed. It is notable to say that different crucial notions in single valued neutrosophic topology were generalized in this article. The family of all single-valued neutrosophic sets on Xis denoted by ξ X

Preliminaries

Some Types of Separation Axioms

Conclusions