In this paper, the concept of neutrosophic 􀀀topological spaces is introduced. We dene and study the properties of neutrosophic 􀀀open sets, 􀀀closed sets, 􀀀interior and 􀀀closure. The set of all generalize neutrosophic pre-closed sets GNPC( ) and the set of all neutrosophic -open sets in a neutrosophic topological space (X; ) can be considered as examples of generalized neutrosophic 􀀀topological spaces. The concept of neutrosophic 􀀀 continuity is dened and we studied their properties. We dene and study the properties of neutrosophic 􀀀 compact, -Lindelof and -countably compact spaces. We prove that for a countable neutrosophic -space X: -countably compactness and -compactness are equivalent. We give an example of a neutrosophic -space X which has a neutrosophic countable -base but it is not neutrosophic -countably compact .