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We develop a dimension theory for D-semianalytic sets over an arbitrary non-Archimedean complete field. Our main results are the equivalence of several notions of dimension and a theorem on additivity of dimensions of projections and fibers in char- acteristic 0. We also prove a parameterized version of normalization for D-semianalytic sets.

Dimension theory and parameterized normalization for D-semianalytic sets over non-Archimedean fields