Aim of this present paper is, we introduce and investigate about new kind of Neutrosophic mapping is called Neutrosophic Regular Weakly Generalized Homoeomorphism in Neutrosophic topological spaces and also discussed about properties and characterization Neutrosophic Regular Weakly Generalized Homoeomorphism.

In this paper, we will define a new class of sets, called fuzzy neutrosophic weakly- generalized closed sets, then we proved some theorems related to this definition. After that, we studied some relations between fuzzy neutrosophic weakly-generalized closed sets and fuzzy neutrosophic α closed sets, fuzzy neutrosophic closed sets, fuzzy neutrosophic regular closed sets, fuzzy neutrosophic pre closed sets and fuzzy neutrosophic semi closed sets.

The idea of neutrosophic generalized homeomorphism is presented in neutrosophic topological spaces. In addition to this, neutrosophic generalized closed and open mappings are also presented. At the same time, their characterizations are discussed by establishing their related attributes.

Smarandache introduced and developed the new concept of Neutrosophic set from the Intuitionistic fuzzy sets. A.A. Salama introduced Neutrosophic topological spaces by using the Neutrosophic crisp sets. In this paper we introduce and study about Neutrosophic Regular Generalized Star b Closed sets in Neutrosophic Topological Spaces and its properties are discussed.

The purpose of this paper is to introduce and study about neutrosophic regular 𝛼 generalized closed sets in neutrosophic topological spaces. Some interesting propositions based on this set are presented and established with suitable examples. Their properties are discussed.

The aim of this paper is to introduce a new class of sets called neutrosophic vague rw closed sets and neutrosophic vague rw-open sets, neutrosophic vague rwT1/2 space and neutrosophic vague rwTw in neutrosophic vague topological spaces. Further we analyse some of its properties.

This paper committed to the investigation of Neutrosophic topological spaces. In this paper Generalized Alpha Closed Sets and Generalized Alpha Open Sets are presented. Some of its properties are contemplated.