A .The notions of ω-µ-closed sets and ω-µ-open sets in generalized topological space were introduced and studied by Al Ghour and Zareer.In this paper, we introduce new classes of ω-µ-open sets and continuous functions in topological spaces and study the characterizations of such ω-µ-open sets and continuous functions in detail.Finally we obtain some decomposition theorems.2020 Mathematics