Neutrosophic μ-Topological spaces

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