Neutrosophic -Topological spaces

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