A new kind of sets called generalized μ-closed (briefly gμ-closed) sets are introduced and studied in a topological space by using the concept of generalized open sets introduced by á. Császár. The class of all gμ-closed sets is strictly larger than the class of all μ-closed sets. Furthermore, g-closed sets (in the sense of N. Levine [17]) is a special type of gμ-closed sets in a topological space. Some of their properties are investigated. Finally, some characterizations of μ_g-regular and μ_g-normal spaces have been given.
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