Śliwa, Wiesław2011-01-132011-01-132004Canad. Math. Bull. 47(2004), 108-118.http://hdl.handle.net/10593/800We prove that there exists a non-archimedean Frechet space U with a basis $(u_n)$ such that any basis $(x_n)$ in a non-archimedean Frechet space X is equivalent to a subbasis $(u_k_n)$ of $(u_n)$. Then any non-archimedean Frechet space with a basis is isomorphic to a complemented subspace of U. Next we prove that there is no nuclear non-archimedean Frechet space H with a basis $(h_n)$ such that any basis $(y_n)$ in a nuclear non-archimedean Frechet space Y is equivalent to a subbasis $(h_k_n)$ of $(h_n)$.enUniversal basesComplemented subspaces with bases