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.

In this paper, we will define a new set called fuzzy neutrosophic strongly alpha generalized closed set, so we will prove some theorems related to this concept. After that, we will give some interesting properties were investigated and referred to some results related to the new definitions by theorems, propositions to get some relationships among fuzzy neutrosophic strongly alpha generalized closed sets, fuzzy neutrosophic closed sets, fuzzy neutrosophic regular closed sets, fuzzy neutrosophic alpha closed sets, fuzzy neutrosophic alpha generalized closed sets and fuzzy neutrosophic pre closed sets which are compared with necessary examples based of fuzzy neutrosophic topological spaces.

As a generalization of fuzzy sets and intuitionistic fuzzy sets, Neutrosophic sets have been developed by Smarandache to represent imprecise, incomplete and inconsistent information existing in the real world. A neutrosophic set is characterized by a truth value, an indeterminacy value and a falsity value. In this paper, we introduce and study a new class of Neutrosophic generalized closed set, namely Neutrosophic generalized pre regular closed sets and Neutrosophic generalized pre regular open sets in Neutrosophic topological spaces.

Papers on neutrosophic programming, neutrosophic hypersoft set, neutrosophic topological spaces, NeutroAlgebra, NeutroGeometry, AntiGeometry, NeutroNearRings, neutrosophic differential equations, etc.

Topology is one of the classical subjects in Mathematics. A lot of researchers have published their ideas. As a generalization of topological concepts many new kind of closed and open sets are published continuously. Salama presented Neutrosophic topological spaces by using Smarandache’s Neutrosophic sets. Many Researchers introduced so many closed sets in Neutrosophic topological spaces. Purpose of this research paper is we introduce Neutrosophic g*-Closed sets and Neutrosophicg*-open sets in Neutrosophic topological spaces. Also we study about study about mappings of Neutrosophic g*-Closed sets.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles in this issue: Neutrosophic Soft Fixed Points, Selection of Alternative under the Framework of Single-Valued Neutrosophic Sets, Application of Single Valued Trapezoidal Neutrosophic Numbers in Transportation Problem.

In this paper, the authors introduced the concept of neutrosophic g -closed sets in neutrosophic topological spaces. Some of their properties and relations with other existing neutrosophic closed were established, some of its characterizations were also investigated.