Continuity is one of most important concepts in many mathematical disciplines. In some situations general notion of continuity is replaced by sequential continuity. Connor and Grosse-Erdmann replaced lim in the definition of sequential continuity of real functions by a linear functional G on a linear subspace of the vector space of all real sequences. Their definition was extended to topological group X by replacing a linear functional G with an additive function defined on a subgroup of the group of all X-valued sequences. In this paper we introduce neutrosophic G-continuity and investigate its properties in neutrosophic topological spaces.

Scientists have always adopted the concept of sequential continuity as an indispensable subject, not only in Topology but also in some other branches of Mathematics. Connor and Grosse-Erdmann gave this concept for real functions by using an arbitrary linear functional G defined on a linear subspace of the vector space of all real sequences instead of lim. Afterwards, this concept were adapted to a topological group X by replacing a linear functional G with an arbitrary additive function defined on a subgroup of the group of all X-valued sequences. Furthermore, alternative theorems in generalized setting were given and varied theorems that had not been achieved for real functions were presented. In this investigation, we offer neutrosophic soft G-continuity and analyze its nature in neutrosophic soft topological spaces.

In this paper, the notions of continuous and irresolute functions in neutrosophic topological spaces are given. Furthermore, we analyze their characterizations and investigate their properties.

In this paper we introduce the concepts of contra 𝛼 generalized continuous mappings and contra 𝛼 generalized irresolute mappings in neutrosophic topological spaces. We also discuss various properties and relations between the newly introduced continuous mappings and the other existing contra continuous mappings in neutrosophic topological spaces.

In this paper we have introduced weakly generalized continuous mappings in neutrosophic topological spaces and analyzed some of their properties. We have discussed some characterizations of weakly generalized continuous mappings in neutrosophic topological spaces.

In this paper we introduce the concept of neutrosophic rw-continuity, neutrosophic rw-open maps and closed maps in neutrosophic topological spaces and some of their properties are discussed.

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. Aim of this paper is we introduce and study the concepts Neutrosophic generalized b closed sets and Neutrosophic generalized b continuity in Neutrosophic topological spaces and its Properties are discussed details.