In this paper, the concept of N-open set in neutrosophic complex topological space is introduced. Some of the interesting properties of neutrosophic complex N-open sets are studied. The idea of neutrosophic complex N-continuous function and its characterization are discussed. Also the interrelation among the sets and continuity are established.

“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.

“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.

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 b generalized closed sets and Neutrosophic b generalized continuity in Neutrosophic topological spaces and its Properties are discussed details.

The article processes the conceptualizations of neutrosophic crisp-open and neutrosophic crisp semi-open sets to define some new types of weakly ”neutrosophic crisp continuity” essentially, neutrosophic crisp *-continuous, neutrosophic crisp-continuous, neutrosophic crisp semi-continuous, neutrosophic crisp semi-continuous and neutrosophic crisp semi-continuous functions. Also, we shall explain the relationships between these types of weakly neutrosophic crisp continuity and the concepts of neutrosophic crisp continuity.

In this paper, the concepts of generalized neutrosophic contra-continuous function, generalized neutrosophic contra-irresolute function and strongly generalized neutrosophic contra-continuous function are introduced. Some interesting properties are also studied.

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.