As a generalization of Fuzzy sets introduced by Zadeh [21] in 1965 and Intuitionistic Fuzzy sets introduced by Atanassav [8] in 1983, the Neutrosophic set had been introduced and developed by Smarandache. A Neutrosophic set is characterized by a truth value (membership), an indeterminacy value and a falsity value (non-membership). Salama and Alblowi [17] introduced the new concept of neutrosophic topological space (NTS) in 2012, which had been investigated recently. In 2018, Parimala M et al. introduced and studied the concept of Neutrosophic homeomorphism and Neutrosophic αψ homeomorphism in Neutrosophic topological spaces. The impact of this article is to introduce and study the concepts of Ngpr homeomorphism and Nigpr homeomorphism in Neutrosophic topological space. Further, the work is extended to Ngpr open mappings, Ngpr closed mappings, Nigpr closed mappings and some of their properties are explored in Neutrosophic topological space.