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In this paper, we introduce the spaces called Strongly-\(T_0^g^* \)-space, Strongly-\(T_1^g^* \)-space and Strongly-\(T_2^g^* \) in topological spaces. Also, we introduce Strongly \(g^*\)-symmetric and studied some of their properties. , number=2, journal=Journal of Informatics and Mathematical Sciences, year=2019, month=Jul., pages=147–154