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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 N αg#ψ-open and N αg#ψ-closed mappings in neutrosophic topological spaces and studied some of their related properties. Further the work is extended to N αg#ψ- homeomorphism, N αg#ψ -C homeomorphism and TN αg#ψ -space in neutrosophic topological spaces and establishes some of their related attributes.