Applications of sets and functions by using an open sets in Fuzzy neutrosophic topological spaces

The definitions provided by the authors of the current study are offered together with a discussion of the recent advances that they have contributed. We begin with an introduction to [Please download the PDF to view the mathematical expression], which includes the concepts of closed and open sets. We explore characteristics in [Please download the PDF to view the mathematical expression] and [Please download the PDF to view the mathematical expression], and provide an idea of obtained results by adding the notion of [Please download the PDF to view the mathematical expression] and analyzing a few of their properties in fnts. We've researched the contrasts between the derived, exterior, and frontier notions that are provided. We also looked at the ideas of ([Please download the PDF to view the mathematical expression]-functions and [[GAMMA].sup.S]-segregated functions and examined and determined the traits. Keywords: [Please download the PDF to view the mathematical expression], derived, exterior, and frontier