In this study, we introduce the concept of neutrosophic connectedness and give some of its characterizations. Additionally, we present neutrosophic product space and show that this type of connectedness is not preserved under neutrosophic product spaces. We also introduce the notions of neutrosophic super-connected spaces, neutrosophic strongly connected spaces and study their properties.

In this article, we introduce neutrosophic closed sets in neutrosophic topological spaces. Also, we introduce and investigate neutrosophic continuous, neutrosophic irresoluteness, neutrosophic connectedness and neutrosophic contra continuous mappings .

Neutrosophic topological structure can be applied in many fields, viz. physics, chemistry, data science, etc., but it is difficult to apply the object with periodicity.

In this paper, the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets are introduced. We also study relations and various properties between the other existing neutrosophic open and closed sets.

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 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.

Neutrosophic α supra-connected space is defined and its properties are studied in this paper. The purpose of this theory is to investigate the common relationship between two objects after dropping an axiom in neutrosophic topological spaces. Also, defined herein is a new compactness in neutrosophic supra topological spaces and some of its properties are investigated.