In this paper, the concept of neutrosophic topological spaces is introduced. We define and study the properties of neutrosophic open sets, closed sets, interior and closure. The set of all generalize neutrosophic pre-closed sets GNPC and the set of all neutrosophic open sets in a neutrosophic topological space can be considered as examples of generalized neutrosophic topological spaces.

In Geographical information systems (GIS) there is a need to model spatial regions with indeterminate boundary and under indeterminacy. The purpose of this chapter is to construct the basic concepts of the so-called "neutrosophic sets via neutrosophic topological spaces (NTs)".

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.

In this disquisition we have scrutinize about the traits of generalized topological spaces using neutrosophic sets. Depending on the nature of neutrosophic sets over the generalized topological spaces, some of the features has been contemplated.

The purpose of this paper is to define the product related neutrosophic topological space and proved some theorems based on this. We introduce the concept of neutrosophic semiopen sets and neutrosophic semi-closed sets in neutrosophic topological spaces and derive some of their characterization. Finally, we analyze neutrosophic semi-interior and neutrosophic semi-closure operators also.

In this paper, the concept of connectedness and compactness on neutrosophic soft topological space have been introduced along with the investigation of their several characteristics. Some related theorems have been established also. Then, the notion of neutrosophic soft continuous mapping on a neutrosophic soft topological space and it’s properties are developed here.

In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.