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This article introduces the concept of neutrosophic b*g α -closed sets, neutrosophic bg -border of a set, neutrosophic b*g α -frontier of a set in neutrosophic topological spaces and the properties of these sets are discussed. The connection between neutrosophic b*g α -border of a set and neutrosophic b*g α -frontier of a set in neutrosophic topological spaces are established.