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. Salama introduced neutrosophic topological spaces by using Smarandache's neutrosophic sets. In this article, we introduce the concept of mathematical expression not reproducible-open and mathematical expression not reproducible-closed mappings in neutrosophic topological spaces and studied some of their related properties. Further the work is extended to mathematical expression not reproducible- homeomorphism, mathematical expression not reproducible-C homeomorphism and mathematical expression not reproducible-space in neutrosophic topological spaces and establishes some of their related attributes. Keywords: mathematical expression not reproducible -open map, mathematical expression not reproducible -closed map, mathematical expression not reproducible -space, mathematical expression not reproducible -homeomorphism, mathematical expression not reproducible-C homeomorphism.