A New Notion of Neighbourhood and Continuity in Neutrosophic Topological Spaces

Abstract

Owing to a wide range of applications in various fields, the neutrosophic theory initiated
by Smarandache has been highly featured in research. This concept led to the evolution of
neutrosophic topological spaces which is being explored extensively. The focus of this paper is to
introduce and study the concept of neutrosophic Υ − neighbourhood and neutrosophic
Υ −continuity in neutrosophic topological spaces. Further, we define the notion of neutrosophic
Υ −irresolute functions. We also observe their attributes and relationship with functions existing in
literature. Moreover, we present some equivalent conditions for the existence of these functions in
which the concept of neighbourhood has been wielded.