On topological classification of non-archimedean Frechet spaces

We prove that any infinite-dimensional non-archimedean Frechet space E is homeomorphic to D-N where D is a discrete space with card(D) = dens(E). It follows that infinite-dimensional non-archimedean Frechet spaces E and F are homeomorphic if and only if dens(E) = dens(F). In particular, any infinite-dimensional non-archimedean Frechet space of countable type over a field K is homeomorphic to the non-archimedean Frechet space K-N.