Inductive and projective limits with partition of unity were introduced and investigated in M. De Wilde [1]. In this note we show that these spaces are complemented subspaces of certain direct sums and products. Especially the function space D(Ω) is a complemented subspace of $$\mathop \oplus \limits_{\text{n}}$$ D(K). Because of this property of these spaces the results in [1] are easy consequences of corresponding results for direct sums and products.